Stats Exam - Descriptives

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A Normal density curve has which of the following properties? Select one: a. It is symmetric. b. It has a peak centered above its mean. c. The spread of the curve is proportional to the standard deviation. d. All of the above

A simple random sample should be used for the t procedure when the sample size is small. Select one: True False

True

To test the null hypothesis in r x c tables, we compare the observed counts with ________ counts.

expected

One of the requirements for the binomial distribution is that the number of observations is _____. Select one: a. fixed b. random c. zero d. continuous

Two sample t procedures are used when _____. Select one: a. subjects are the same in both samples b. subjects in one sample are completely unrelated to the subjects in the other sample c. Subjects are similar in both samples d. None of the above.

A coin is about to be tossed multiple times. Assume the coin is fair, i.e., the probability of heads and the probability of tails are both 0.5. Reference: Ref 5-24 If the coin is tossed 60 times, what is the probability that less than ⅓ of the tosses are heads? Select one: a. 0.0031 b. 0.0067 c. 0.109 d. 0.344

If you have two groups to compare, the square of the t test for independent groups and the ____ test are essentially the same when the alternative hypothesis is two-sided test.

Since confidence intervals are based on the sampling distribution of the sample mean, it is possible to form confidence intervals when sampling from slightly skewed distributions due to the central limit theorem. Select one: True False

True

The basic principle of an ANOVA is to compare the variability of the observations among groups to the variability within groups. True or False

True

The researcher tests the following hypotheses: H0 : μ1 = μ2, Ha : μ1 ≠ μ2The 90% confidence interval is 2 ± 0.83 meters. Based on this confidence interval, Select one: a. we would reject the null hypothesis of no difference at the 0.10 level. b. the P-value is less than 0.10. c. neither a nor b is correct. d. both a and b are correct.

By doing multiple comparisons when there are more than two experimental groups, we increase the risk of making what kind of mistake? Select one: a. Accepting H0 b. Type I error c. Type II error d. All of the above.

A comprehensive report called the Statistical Report on the Health of Canadians was produced in 1999. In it was reported that 42% of Canadians, 12 years of age or older, had their most recent eye examination within the previous year. What is the approximate probability that the count of the number of people in the sample of size 100 who had their most recent eye examination in the previous year is more than 38? Select one: a. 0.759 b. 0.271 c. 0.729 d. 0.209 e. .8188

A national poll of 600 men announced that the proportion in the survey who claimed to help their wives at home was 85%. If we took a larger poll of 1200 men, what will be the standard deviation of the number of men who help at home, based on the first survey? Select one: a. 12.37 b. 17.32 c. 153

A poll finds that 54% of the 600 people polled favor the incumbent. Shortly after the poll is taken, it is disclosed that he had an extramarital affair. A new poll finds that 50% of the 1030 polled now favor the incumbent. We want to know if his support has decreased. The test statistic is Select one: a. z = 1.56. b. z = -2.57. c. z = -1.55.

One sample t test procedures are for use on subjects that are _______. Select one: a. independent b. the same or similar c. binomial d. None of the above.

For each of the following scenarios, select if the binomial distribution is the appropriate distribution for the random variable X. Select one or more: a. A fair coin is flipped 10 times. Let X = the number of times the coin comes up tails. b. A fair coin is flipped multiple times. Let X = the number of times the coin needs to be flipped until we see 10 tails. c. A roulette wheel with one ball in it is turned six times. Let X = the number of times the ball lands on red. d. There are 10 people in the room: five men and five women. Three people are to be selected at random to form a committee. Let X = the number of men on the three-person committee.

A and C

For this example, we notice that Select one: a. this is an observational study. b. the data show no evidence of a violation of the assumption that the four populations have the same standard deviation. c. ANOVA can be used on these data because ANOVA requires that the sample sizes are equal. d. None of the above

Two neighboring towns share a school district. A group of students at the high school is doing a study on the income in the two towns. Based on what they learned in their statistics class, they will assume that the distribution of income is right-skewed. However, large samples should allow them to perform a two-sample t test for equality of average household income. Let the μ1 denote the average household income of town X and μ2 the average household income for town Y. The hypotheses that the group of students will test are H0: μ1 = μ2 versus Ha: μ1 ≠ μ2. A 95% confidence interval for the difference in average household income in the two neighboring towns is (4.5721, 9.8279). What can be said (with certainty) about the value of the P-value for testing the hypotheses H0: μ1 = μ2 versus Ha: μ1 ≠ μ2? Select one or more: a. < 0.01 b. < 0.05 c. < 0.10 d. > 0.01 e. > 0.05 f. > 0.10

B and C

An instructor wanted to construct a confidence interval for the mean GPA of the students in his class. He used the campus records system to obtain their GPA's and computed the 95% interval as (2.32, 2.87). If he wants to use this interval to describe the students in his class, Select one: a. he's 95% confident the interval contains the real average GPA. b. there's a 5% chance the interval is wrong. c. he didn't need an interval after all.

A 99% confidence interval for the mean μ of a population is computed from a random sample and found to be 6 ± 3. We may conclude that Select one: a. there is a 99% probability that μ is between 3 and 9. b. the true mean is 6 and the true margin of error is 3, both with 99% probability. c. if we took many, many additional random samples, and from each computed a 99% confidence interval for μ, approximately 99% of these intervals would contain μ. d. All of the above

A college basketball player is known to make 80% of his free throws. Reference: Ref 5-28 Over the course of the season, he will attempt 100 free throws. Assuming free-throw attempts are independent, what is the probability that the number of free throws he makes exceeds 80? Select one: a. 0.2000 b. 0.2266 c. .4602 d. 0.7734

A drug manufacturer wishes to compare the incidence of side-effects from two different formulations of a drug. In a sample of 400 patients using formulation 1, there are 20 patients who experience side-effects. In a sample of 100 patients using formulation 2, there are 10 patients who experience side-effects. The p-value for a test of no difference in side-effect rates between the two formulations is 0.06. Which of the following is correct? Select one: a. There is a 6% chance that formulation 2 has a larger side-effect rate than formulation 1. b. The side-effect rate of formulation 2 is 6% larger than that of formulation 1. c. The chance of seeing a 5-percentage-point difference or larger is 6% if the two formulations have the same side-effect rate. This is correct. Text reference: Section 20.5 Significance Tests for Comparing Proportions d. Six percent of patients overall experienced side-effects.

Researchers wish to examine the effectiveness of a new weight-loss pill. A total of 200 obese adults are randomly assigned to one of four conditions: weight-loss pill alone, weight-loss pill with a low-fat diet, placebo pill alone, or placebo pill with a low-fat diet. The weight loss after 6 months of treatment is recorded in pounds for each subject. To analyze these data, you would use Select one: a. a z test. b. a t test. c. an ANOVA F test. d. a chi-square test.

The p-values for the goodness of fit test are computed from which distribution? Select one: a. Normal b. Binomial c. Chi-square d. Uniform

There is an old saying in golf: "You drive for show and you putt for dough." The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data on the top 69 money winners on the PGA tour in 1993 are examined. The average number of putts per hole for each player is used to predict the total winnings (in thousands of dollars) using the simple linear regression model(1993 winnings)i = β0 + β1(average number of putts per hole)i + εiwhere the deviations εi are assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software: R2 = 0.081 s = 281.8 Variable Parameter estimate Standard error Constant 7897.2 3023.8 Average putts -4139.2 1698.4 Reference: Ref 10-1 Which of the following conclusions seems most justified? Select one: a. There is no evidence of a relation between the average number of putts per round and the 1993 winnings of PGA tour pros. b. There is distinct evidence (P-value less than 0.05) that there is a positive correlation between 1993 winnings and average number of putts per round. c. There is some evidence that PGA tour pros who averaged fewer putts per round had higher winnings in 1993. d. The presence of strongly influential observations in these data makes it impossible to draw any conclusions about the relationship between 1993 winnings and average number of putts per round.

Which assumption is behind inference for linear regression? Select one: a. The residuals have a t distribution. b. The data is Normally distributed. c. The residuals are N(0, σ).

Which of the following statements is (are) TRUE? Select one or more: a. The margin of error for a 95% confidence interval for the mean μ increases as the sample size increases. b. The margin of error for a confidence interval for the mean μ, based on a specified sample size n, increases as the confidence level decreases. c. The margin of error for a 95% confidence interval for the mean μ decreases as the population standard deviation decreases. d. The sample size required to obtain a confidence interval of specified margin of error m increases as the confidence level increases.

C, D

A fair die is rolled 12 times. Let X = the number of times an even number occurs on the 12 rolls. What is the appropriate distribution for the random variable X? Select one: a. A binomial distribution with a mean of 2. b. A binomial distribution with a standard deviation of 3. c. A binomial distribution with a mean of 0.5. d. A binomial distribution with a mean of 6.

The difference between a sample mean and the population mean may be referred to as ______________________. Select one: a. the standard deviation b. the variance c. skewness d. sampling error

One condition for inference on p is that the population is at least 10 times as large as the sample used for inference. Select one: True False

False

Outliers do not have a large effect on the formation of confidence intervals. Select one: True False

False

Possible values for the counts in a binomial distribution range from -∞ to ∞. Select one: True False

False

The binomial distribution is best for modeling the number of successes in a binomial or Normal setting.

False

The central limit theorem does not apply to discrete random variables. True or false?

False

The large sample z significance test for population proportion is best used when the sample size n is greater than 30. Select one: True False

False

The purpose of forming confidence intervals is to find the exact value of the true population mean based on a random sample. Select one: True False

False

The results obtained from a Z test of significance can always be trusted as long as you use a random sample. Select one: True False

False

When forming confidence intervals, it is very important that you only take large samples from Normal populations. Select one: True False

False

When the underlying assumptions for the use of t procedures are not exactly met, the probability calculations are still valid as long as the data are very close to Normal. Select one: True False

False

The chi-square distribution is described by a single parameter called the _______. Select one: a. degree of freedom b. mean c. variance d. None of the above.

Which of the following statements about Normal quantile plots is (are) TRUE? Select one or more: a. The Normal quantile plot is a very useful graphical tool for assessing the adequacy of the Normal model. b. If the points on a Normal quantile plot lie close to a straight line, the plot indicates that the Normal model is an adequate representation for the data. c. Because you will see the usual mound-like appearance of the Normal distribution on a histogram, it is more helpful than the quantile plot for assessing Normality. d. On a quantile plot, outliers will appear as points that are far away from the overall pattern of the plot.

A, B, and D

A statistic is said to be unbiased if Select one: a. the survey used to obtain the statistic was designed to avoid even the hint of racial or sexual prejudice. b. the mean of its sampling distribution is equal to the true value of the parameter being estimated. c. both the person who calculated the statistic and the subjects whose responses make up the statistic were truthful. d. it is used for only honest purposes.

There are twenty multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth 5 points and only one response per question is correct. Suppose a student guesses the answer to each question, and her guesses from question to question are independent. On average, this strategy will result in a mean score of Select one: a. 5. b. 25. c. 50.

A set of 10 cards consists of five red cards and five black cards. The cards are shuffled thoroughly. Reference: Ref 5-20 One card is to be selected at random. The color will be observed and the card replaced in the set. The cards are then thoroughly reshuffled. This selection procedure is repeated four times. Let X = the number of red cards observed in these four trials. What is the mean of X? Select one: a. 0.5 b. 1 c. 2 d. 4

For small samples, t intervals are ___________ z intervals based on the same data set. Select one: a. narrower than b. the same as c. wider than

Let X be a binomial random variable with distribution B(10, 0.6). What is the probability that X equals 8? Select one: a. b. c. d. e. None of the above.

C 45(0.6)^8(0.4)^2

A sample of size n is selected at random from a population that has mean μ and standard deviation σ. The sample mean will be determined from the observations in the sample. Which of the following statements about the sample mean, , is (are) TRUE? Select one: a. The mean of is the same as the population mean, i.e., μ. b. The variance of is . c. The standard deviation of decreases as the sample size grows larger. d. All of the above are true. e. Only A and B are true.

A test of significance was conducted in a study involving a random sample of 25 subjects. Based on the test result using the sample mean, , it was determined that the P-value was equal to 0.028. Which of the following statements about this P-value is (are) TRUE? Select one: a. In this situation there is relatively strong evidence against the null hypothesis. b. The P-value was calculated under the assumption that the null hypothesis was true. c. The probability of a value of the test statistic at least as extreme as that observed in this study, assuming the null hypothesis is true, is 0.028. d. All of the above are true statements.

Which of the following is not a requirement for the validity of the chi-square goodness of fit test? Select one: a. Independent observations b. A fixed number of observations c. All observations fall into one of k outcome classes d. Normally distributed data

Large sample confidence intervals are best used when the number of successes and the number of failures are greater than 5? Select one: True False

False

A lab scientist is interested in whether lab rats that grow up alone are smaller than lab rats that grow up with other rats around them to play with. He randomly selects 10 young rats with approximately the same age and size. Five of these will spend the next four months by themselves and the other five rats will each have three other rats to play with during that same time. After four months, the scientist measures the abdomen circumference of all the rats (in mm). The results are shown below: Alone group (#1) 110 123 113 103 120 Play group (#2) 119 125 131 128 136 The sample means and sample standard deviations are = 113.8 and s1 = 7.98, = 127.8 and s2 = 6.38 The sample standard deviations are fairly close in value. It seems reasonable based on these estimates to assume the variances in both populations are equal. What can we say about the value of the P-value (rounded to 4 decimal places)?

.0078

It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home. Reference: Ref 5-19 What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?

0.000000006

Chromosome defect A occurs in only one out of 200 adult males. A random sample of 100 adult males is selected. Let the random variable X represent the number of males in the sample who have this chromosome defect. Reference: Ref 5-15 What is the standard deviation of the random variable X?

0.705

It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home. Reference: Ref 5-19 What is the probability that more than 20% of the young adults in a simple random sample of 100 do not own a landline?

Recent revenue shortfalls in a Midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25% tuition increase. It was determined that such an increase was needed to simply compensate for the lost support from the state. Random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether or not they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are given in the following table: Year in school Opinion Freshman Sophomore Junior Senior Strongly opposed 39 36 29 18 Not strongly opposed 11 14 21 32 Reference: Ref 9-8 At the 5% significance level, what is the largest value the chi-square statistic could be, before rejecting the null hypothesis? Select one: a. 7.81 b. 9.25 c. 9.49 d. 16.92 Clear my choice

7.81

A TV news program conducts a call-in poll about a proposed city ban on smoking in public places. Of the 2467 callers, 1900 were opposed to the ban. Which of the following assumptions for inference about a proportion using a confidence interval are violated? Select one: a. The data are an SRS from the population of interest. b. The population is at least 10 times as large as the sample. c. n is so large that both the count of successes, and the count of failures, are 10 or more. d. There appear to be no violations.

A popular Web site among college students is www.studentinfo.com. It lists information about jobs both in the United States and abroad. The management of the Web site claims that half of all college students know about it. You do not quite believe this and think it is much less than half. You decide to ask a sample of 10 students if they know about the Web site. Out of the 10 students asked, only two had heard of the Web site. Reference: Ref 5-26 If the management of the Web site is correct about the proportion of students who know about the Web site, what is the probability that you would find only two students who know about the Web site in a simple random sample of 10 students? Select one: a. 0.044 b. 0.055 c. 0.115 d. 0.244

A sample of 50 male and 50 female infants were put on an experimental infant formula. After two weeks the parents of each infant were asked to fill out a questionnaire concerning infant satisfaction on the formula. One of the questions was "Did Baby Seem to Like the Formula?" with possible responses 1 - Like Very Much 2 - Like Somewhat 3 - Neutral 4 - Dislike Somewhat 5 - Dislike Very Much The appropriate null hypothesis for this data is that Select one: a. the distribution of parents' responses on this question is the same for male and female infants. b. the distribution of gender is the same for each parents' response to this question. c. gender and parents' responses on this question are independent.

A simple random sample of five female basketball players is selected. Their heights (in cm) are 170, 175, 169, 183, and 177. What is the standard error of the mean of these height measurements? Select one: a. 2.538 b. 2.837 c. 5.075 d. 5.675 e. Cannot be determined

A study examined the effectiveness of Botox injections in the corrugator supercilii muscles for the treatment of chronic migraines. Of the 29 migraine-prone patients participating in the study, 24 reported some form of improvement. Suppose 95% confidence interval for the population proportion of migraine patients who benefit from such Botox injections is found to be (.65, .93). We cannot conclude from the findings that Botox injections in the corrugator supercilii muscles are the cause for these improvements, because Select one: a. there is no comparison group, and the improvements could simply reflect the placebo effect. b. we only computed a confidence interval, not a P-value. c. we are only 95% confident that our interval captures the true population parameter. d. the sample size is too small.

A study to compare two types of infant formula was run at two sites, one in Atlanta and the second in Denver. The study was run over a three-week period. Subjects at both sites were classified as dropouts if they left the study before the conclusion, or completers if they finished the study. The following table gives the number of dropouts and completers at each site. A chi-square test was performed and the result was X2 = 5.101 with P-value = 0.024. Responder DropoutCompleterAtlanta16134Denver21379 The correct conclusion is Select one: a. Atlanta had a greater dropout rate. b. Denver had a greater dropout rate. c. any differences can be explained by sampling variability.

A study was conducted at the University of Waterloo on the impact characteristics of football helmets used in competitive high school programs. There were three types of helmets considered, classified according to liner type: suspension, padded-suspension, and padded. In the study, a measurement called the Gadd Severity Index (GSI) was obtained on each helmet using a standardized impact test. A helmet was deemed to have failed if the GSI was greater than 1200. Of the 81 helmets tested, 29 failed the GSI 1200 criterion. Reference: Ref 8-9 If the test was to be conducted again, how many suspension-type helmets should be tested so that the margin of error does not exceed 0.05 with 95% confidence? Select one: a. 385 b. 20 c. 271 d. 250 e. 82 Clear my choice

A survey of food allergies in a random sample of 184 young children found that 13 had some food allergy. Reference: Ref 19-3 We should use the plus four method to compute a 95% confidence interval for the population proportion of young children who have a food allergy, because Select one: a. the counts of successes and failures in the sample are too low for the large-sample method. b. the sample size is too small for the large-sample method. c. we do not know sigma, the population standard deviation. d. we do not know that population proportion of young children who have a food allergy.

Based on surveys conducted in 1989 and 1999, a researcher compared the proportion of high school age females interested in a career in science in 1989 with the proportion in 1999. He concluded that the proportions were not significantly different at the α = 0.05 level because the P-value was 0.121. Assuming the surveys were simple random samples from the appropriate populations, we may conclude Select one: a. that the probability of observing a difference at least as large as that observed by the researcher if, in fact, the two proportions were equal is 0.121. b. that in repeated sampling, the researcher would obtain the difference actually observed in approximately 12.1% of the samples. c. very little. Without knowing if the observed difference is practically significant, we cannot assess whether the results are statistically significant.

Data on the water quality in the eastern United States was obtained by a researcher who wanted to ascertain whether or not the amount of particulates in water (ppm) could be accurately used to predict water quality score. Suppose we fit the following simple linear regression model Qualityi = β0 + β1 × particulatesi + εi where the deviations εi were assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software based on a sample of size 61. Variable Estimate Std. error of estimate Constant 6.214 1.003 Particulates -0.009 0.020 R2 = 0.005, s = 0.7896 Reference: Ref 23-2 Here is a scatterplot of the amount of particulates versus water quality. Which of the following statements is supported by the plot? Select one: a. There is no striking evidence in the plot suggesting that the assumptions for regression are violated. b. There appears to be a serious outlier in the plot, suggesting that our results above must be interpreted with caution. c. The plot contains dramatic evidence that the standard deviation of the response about the true regression line is not even approximately the same everywhere. d. The plot contains many fewer points than were used to fit the least-squares regression line in the previous problems. Obviously, there is a major error present.

From previous polls, it is believed that 66% of likely voters prefer the incumbent. A new poll of 500 likely voters will be conducted. In the new poll, if the proportion favoring the incumbent has not changed, what is the mean and standard deviation of the number preferring the incumbent? Select one: a. μ = 330, σ = 10.59 b. μ = 0.66, σ = 0.021 c. μ = 330, σ = 18.17

In a certain game of chance, your chances of winning are 0.2. Assume outcomes are independent and that you will play the game five times. Reference: Ref 5-22 What is the probability that you win all five times? Select one: a. 0.00032 b. 0.04 c. 0.3277 d. 0.6723

In a sample of 20 items, I found 6 defective. In constructing a confidence interval for the proportion of defectives, I should use Select one: a. the plus four method. b. the large sample interval. c. neither of the two methods.

It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home. Reference: Ref 5-19 What is the probability that everyone in a simple random sample of 100 young adults owns a landline? Select one: a. Less than .001 b. 1 c. .5 d. None of the above.

Large sample significance tests for a single proportion are based on the _______. Select one: a. z statistic b. binomial distribution c. t- test d. uniform distribution

Let X be a random variable with a binomial distribution B(24, 0.4). Then, the proportion has a mean and a standard deviation, respectively: Select one: a. 0.4, 0.1. b. 0.4, 0.01. c. 0.4, 2.4. d. 9.6, 5.76. e. 9.6, 2.4

Many studies have suggested a link between exercise and healthy bones because exercise stresses the bones and this causes them to become stronger. A study randomized 30 subjects to a control (no additional exercise), low-impact, and high-impact aerobics and measured the change in bone density. The ANOVA p-value was 0.023. Which of the following is correct? Select one: a. The significant p-value only indicates that there is evidence that at least one pair of means are different. It doesn't indicate which of the means are different. b. A multiple comparison procedure is needed because the p-value indicates that the means could all be the same. c. The Analysis of Variance (ANOVA) method tests to see if the variances in the groups could be the same. d. The results could be suspect because 30 people represents too small of a sample to ensure that the results are representative.

One assumption in ANOVA is that the populations have equal standard deviations. Side-by-side boxplots of the sample data are shown below. Does this assumption seem reasonable? Select one: a. Yes, because the interquartile ranges are similar in the graph. b. No, because there is an outlier present in the data. c. No, because medians for the three different brands are so different. d. This cannot be determined without studying the actual data values.

Sale of eggs that are contaminated with salmonella can cause food poisoning among consumers. A large egg producer takes an SRS of 200 eggs from all the eggs shipped in one day. The laboratory reports that 11 of these eggs had salmonella contamination. Unknown to the producer, 0.2% (two-tenths of one percent) of all eggs shipped had salmonella. In this situation Select one: a. 0.2% is a parameter and 11 is a statistic. b. 11 is a parameter and 0.2% is a statistic. c. both 0.2% and 11 are statistics. d. both 0.2% and 11 are parameters.

Suppose that examination of the residual plots from an ANOVA indicate serious problems with both normality and homogeneity of variances. What might you do to provide a solution to this problem? Select one: a. Transformation of the dependent variable. b. Transformation of the independent variable. c. Transformation of the independent and dependent variables.

The University of Chicago's General Social Survey (GSS) is the nation's most important social science sample survey. The GSS regularly asks its subjects their astrological sign. Since the 12 zodiac signs evenly divide the calendar year, this information can be used to test whether births are uniformly distributed across the year. Here is an incomplete Minitab output for the corresponding chi-square test: Test ContributionCategory Observed Proportion Expected to Chi-SqAquarius 224 0.0833333 231.583 0.248Aries 225 0.0833333 231.583 0.187Cancer 240 0.0833333 231.583 0.306Capricorn 216 0.0833333 231.583 1.047Gemini 241 0.0833333 231.583 0.383Leo 260 0.0833333 231.583 3.487Libra 243 0.0833333 231.583 0.563Pisces 244 0.0833333 231.583 0.666Sagittarius 200 0.0833333 231.583 4.307Scorpio 214 0.0833333 231.583 1.335Taurus 222 0.0833333 231.583 0.397Virgo 250 0.0833333 231.583 1.465 N DF Chi-Sq P-Value2779 * * * Reference: Ref 21-1 The chi-square test is in this situation Select one: a. is valid, because the sample is random and the expected counts are large enough. b. is valid, because the sample is random and the observed counts are large enough. c. is valid, because the sample size is large. d. is not valid, because we do not know the true population proportions.

The birth weights of a random sample of 26 baby boys are displayed in the following Normal quantile plot. Based on the graph, we determine that a. the data have a low outlier. b. the data are approximately Normal c. the data are skewed to the right. d. the data are bimodal.

We want to assess possible side effects of the drug nifedipine used to reduce chest pain in patients with angina. A study measures the heart rate in beats per minute of patients with angina before and after being treated with nifedipine. To estimate the proportion of subject whose heart rate increases after taking nifedipine, we should use Select one: a. a one-sample z procedure for a proportion. b. a two-sample z procedure for proportions. c. a one-sample or matched pairs z or t procedure for a mean. d. a two-sample z or t procedure for means.

When calculating a sample size to obtain a confidence interval with a specified margin of error m, which of the following choices of the hypothesized proportion, p*, will result in the smallest sample size? Select one: a. larger than 0.7 or smaller than 0.3 b. 0 c. 0.5 d. Any guessed value

Which of the following statements about the sums of squares associated with the analysis of variance is (are) FALSE? Select one: a. The total variation in the data is always equal to the among-group variation minus the within-group variation. b. SSG measures the variation of the group means around the overall mean, . c. SSE measures the variation of each observation around its group mean, . d. SST measures variation of the data around the overall mean, . e. SST = SSG + SSE

A comprehensive report called the Statistical Report on the Health of Canadians was produced in 1999. In it was reported that 42% of Canadians, 12 years of age or older, had their most recent eye examination within the previous year. Reference: Ref 5-30 If a random sample of 20 Canadians in this age group were selected, the probability that 6, or 30%, of the selected individuals would have had their most recent eye examinations in the previous year would be: Select one: a. . b. . c. . d. . e. .

A (20 / 6)(.42)^6(.58)^14

In a study on scholastic test scores of entering college freshmen, a random sample of colleges across the nation is selected and the average SAT Math score for the freshman class is recorded. The colleges are categorized according to their affiliation: Public, Private, or Church. Does it appear that freshmen entering the three different types of schools do equally well on the SAT Math? Computer output is included below: Source Sum of squares DF Mean square F P-value Groups 63906.2 2 31953.1 5.696 0.005 Error 353440.2 63 5610.2 Total 417346.4 65 Reference: Ref 12-4 One of the assumptions in ANOVA is that the population standard deviations are equal. Which of the following statements are true? You may select zero, one, or more boxes. Select one or more: a. We may use side-by-side boxplots to assess if this assumption of equal population standard deviations seems reasonable. b. As long as the ratio of the largest to the smallest sample standard deviation is greater than 2, then the assumption seems to be satisfied. c. An estimate for the common standard deviation σ in the three populations equals 74.90. d. We may use Normal quantile plots to determine if the assumption of equal population standard deviations is reasonable.

A and C

Do heavier cars use more gasoline? To answer this question, a researcher randomly selected fifteen cars. He collected their weight (in hundreds of pounds) and the mileage (MPG) for each car. From a scatterplot made with the data, a linear model seemed appropriate. The following output was obtained from SPSS: Reference: Ref 10-5 Which of the following statements is (are) true? Select one or more: a. The explanatory variable in this study is the weight of the car. b. The value of the correlation between weight and mileage is 0.662. c. An estimate for the standard deviation σ of the deviations εi in the linear regression model is 6.275. d. Approximately 43.8% of the variation in mileage is accounted for by the linear relationship with the weight of the car.

A and D

A fire insurance company wishes to study the amount of fire damage in major residential fires. The data they collected from a simple random sample of fires in the past six months are shown below: Damage (in thousands of dollars) 26.2 17.8 23.1 36.0 31.1 43.2 36.4 26.1 The fire chief wishes to estimate the mean amount of damage with a 95% confidence interval and computes it to be (23.075, 36.9). Suppose we wish to test if the mean amount of damage equal to $30,000 or not. Based on the previously calculated confidence interval, what would we conclude at the .05 significance level? Select one: a. There is sufficient evidence to conclude the mean amount of damage in the population is $30,000. b. There is insufficient evidence to conclude the mean amount of damage in the population is $30,000. c. There is not enough information to draw a conclusion regarding the test using the confidence interval only.

A high school has 1000 students. As a school project, the school conducts a mock lottery. Each student in the school is asked to select an integer between 1 and 1000, independently of the choices of the other students. Each student gives their selection, with their name, to the school principal. The school principal uses a random number generator to select an integer between 1 and 1000 and any student that picked this number is declared a winner. What is the probability that no student wins? Select one: a. 0. There are 1000 students and 1000 numbers, so some student must win. b. (0.999)1000 c. 0.1587

A national polling agency conducted a poll in which an SRS of 3000 Americans that are registered to vote were contacted regarding whether additional taxes should be imposed on gasoline to encourage individuals to purchase more fuel-efficient automobiles. The agency obtained answers from 1200 Americans and found that 580 would vote for the proposed taxes. Let p represent the proportion of registered voters that would vote for the proposed taxes. Reference: Ref 19-9 One concern with this study may be that Select one: a. it only included Americans. b. the nonresponse rate was 60%. c. no inference methods can be used since the proportion in favor was not 50%. d. None of the above

A simple random sample of 10 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago. The sample mean was 7 years with a standard deviation of 2 years. Assume the distribution of the time the employees have worked for the postal service is approximately Normal. The hypotheses being tested are H0: μ = 7.5, Ha: μ ≠ 7.5. What is a 95% confidence interval for μ, the population mean time the postal service employees have spent with the postal service? Select one: a. 7 ± 1.24 b. 7 ± 1.43 c. 7 ± 0.4 d. 7 ± 0.2

A simple random sample of 450 residents in the state of New York is taken to estimate the proportion of people who live within one mile of a hazardous waste site. Reference: Ref 8-2 If a 95% confidence interval were calculated for a scenario where p= 0.3 and another scenario where p= 0.7, how would the two confidence intervals compare? Select one: a. Since the sample proportion in the first scenario is smaller, its confidence interval would be narrower. b. Even though the sample proportions are different, the widths of the confidence intervals would be equal. c. Since the sample proportion in the second scenario is larger, its confidence interval would be shifted to the right and narrower than the one calculated from the first scenario. d. This cannot be determined from the information given.

A sociologist is studying the effect on the divorce rate of having children within the first three years of marriage. From city marriage records she selects a random sample of 400 couples who were married between 1985 and 1990 for the first time, with both members of the couple between 20 and 25. Of the 400 couples, 220 had at least one child within the first three years of marriage. Of the couples who had children, 83 were divorced within 5 years, while in the couples who didn't have children within three years only 52 were divorced. Suppose p1 is the proportion of couples married in this time-frame who had a child within the first three years and were divorced within five years and p2 is the proportion of couples married in this time-frame who did not have a child within the first three years and were divorced within five years. The sociologist hypothesized that having children early would increase the divorce rate. She tested the one-sided alternative and obtained a P-value of 0.0314. The correct conclusion is that Select one: a. if you want to decrease your chances of getting divorced, it is best to wait several years before having children. b. there is evidence of an association between divorce rate and having children early in a marriage. c. if you want to decrease your chances of getting divorced, it is best not to marry until you are closer to 30 years old.

A study recorded the body mass index (BMI) of a random sample of 200 American men and 200 American women. Individuals with a BMI above 30 are considered obese. To estimate the difference in the percent of individuals who are obese among American men and American women, you should use Select one: a. a one-sample z procedure for a proportion. b. a two-sample z procedure for proportions. c. a one-sample or matched pairs z or t procedure for a mean. d. a two-sample z or t procedure for means.

A study was conducted to determine if taking a popularly advertised herbal supplement will result in weight loss in obese males. A random sample of clinically obese males was obtained. Each subject was weighed before taking the supplement and again after 60 days using the supplement. Subjects were told not to alter their diet in any way during the study period. The following table shows the observed results for the six subjects: Subject 1 2 3 4 5 6 Before (B) 164 172 186 166 174 178 After (A) 166 154 176 170 160 168 D = B - A -2 18 10 -4 14 10 Reference: Ref 7-10 With α = 0.05, what observed values of the test statistic would cause the sample results to be declared statistically significant? Select one: a. z > 1.645 b. t > 2.015 c. t > 1.796 d. z > 1.960 e. | t | > 2.571

A study was performed to examine the personal goals of children in grades 4, 5, and 6. A random sample of students was selected for each of the grades from schools in Georgia. The students received a questionnaire regarding personal goals. They were asked what they would most like to do at school: make good grades, be popular, or be good at sports. Results are presented in the table below by the sex of the child. Make good gradesBe popularBe good in sportsBoys963294Girls2954540 This is a Select one: a. 2 × 2 table. b. 2 × 3 table. c. 3 × 2 table.

An inspector inspects large truckloads of potatoes to determine the proportion p with major defects prior to using the potatoes to be made into potato chips. She intends to compute a 95% confidence interval for p. To do so, she selects an SRS of 50 potatoes from the over 2000 potatoes on the truck. Suppose that only 2 of the potatoes sampled are found to have major defects. Which of the following assumptions for inference about a proportion using a confidence interval are violated? Select one: a. The population is at least 20 times as large as the sample. b. n is so large that both the count of successes n and the count of failures n (1 - ) are 10 or more. This answer is correct. n here is 50. The proportion of potatoes in the sample with major defects is = 2/50, so n = 2, which is less than 10.Text reference: section 8.1. c. There appear to be no violations.

Are different species of mosquitoes attracted differently to the two sexes? A study was conducted where three closely related species of mosquitoes were presented with an arm from a male or a female and the selection was recorded. Here is the two-way table of counts: FemaleMaleSpecies A24866Species B514105Species C351225Which of the following is correct? Select one: a. The chi-square test may not be completely appropriate because the smallest cell count is less than 100. b. The chi-square test may not be completely appropriate because each arm has several bites. c. The chi-square test may not be completely appropriate because all species bite both types of arms. d. The chi-square test may not be completely appropriate because the table is not a 2 x 2 table.

Check the box next to statements that are true. Select one or more: a. This is a randomized, designed experiment. b. The data show no strong evidence of violating the assumption that the three populations have the same standard deviation. c. ANOVA cannot be used on these data because the sample sizes are different. d. ANOVA cannot be used on these data because the data show very strong evidence of non-Normal population distributions.

Correct 1.00 points out of 1.00 Flag question Question text Echinacea is widely used as an herbal remedy for the common cold, but does it work? In a double-blind experiment, healthy volunteers agreed to be exposed to common-cold-causing rhinovirus type 39 and have their symptoms monitored. The volunteers were randomly assigned to take either a placebo or an echinacea supplement daily for 5 days following viral exposure. Among the 103 subjects taking a placebo, 88 developed a cold, whereas 44 of the 48 subjects taking echinacea developed a cold. Which of the following is correct? Select one: a. The large-sample confidence interval for the difference in proportions can be used because the sample sizes are large in each group. b. The "plus 4" confidence intervals should be used because the number of subjects that did not develop a cold in the echinacea group is less than 10. This is correct. Text reference: Section 20.4 Accurate Confidence Intervals for Comparing Proportions c. The "plus 4" confidence intervals should be used because the sample sizes in each group are less than 150. d. The large-sample confidence interval for the difference in proportions requires that the data are Normally distributed.

It is claimed that 55% of marriages in the state of California end in divorce within the first 15 years. A large study was started 15 years ago and has been tracking hundreds of marriages in the state of California. Reference: Ref 5-25 Suppose 10 marriages are randomly selected. What is the probability that less than two of them ended in a divorce? Select one: a. 0.0021 b. 0.0045 c. 0.0130 d. 0.0274

Mice populations rise and fall with the abundance of acorns, their favored food. Experimenters studied two similar forest areas in a year when the acorn crop failed. They added hundreds of thousands of acorns to one area to imitate an abundant acorn crop, while leaving the other area untouched. The next spring, 54 of the 72 mice trapped in the first area were in breeding condition, versus 10 of the 17 mice trapped in the second area. The following output is from an analysis of this data:Which of the following is correct? Select one: a. The relative risk measures the ratio of the probability of breeding with added acorns to the control group. b. The estimated probability of breeding if acorns are added is about 1.27 times greater than in the control area. c. Because the confidence interval for the relative risk does not include the value of 0, there is evidence that the breeding rates are different in the two areas. d. Because the confidence interval for the risk difference excludes the value of 1, there is evidence that the breeding rates are the same in both areas.

Resource-selection analysis compares the distributions of animals relative to the distribution of habitat. If the two don't agree, there is evidence of selection. A survey of 106 moose found that 24 were located in "In burn - interior," 22 in "In burn - edge," 20 in "Out of burn - edge," and 40 in "Other" habitat types. The corresponding proportion of the landscape as determined by a Geographic Information System (GIS) in these habitats was 0.340, 0.101, 0.104, and 0.455 respectively. The p-value for the goodness-of-fit test is Select one: a. There is less than a 1% chance that the moose have expressed any selection. b. If the moose do not express a selection for habitat, there is less than a 1% chance of seeing these observed locations. c. There is less than a 1% chance that the moose have not expressed any selection. d. If the moose express resource selection, then there is less than a 1% chance we would observe this data.

Suppose we roll a fair six-sided die ten times. What is the probability that even numbers occur exactly the same number of times as do odd numbers on the ten rolls? Select one: a. 0.1667 b. 0.2461 c. 0.3125 d. 0.5000

The Big Smiles Portrait Studio is conducting a survey among their clients. One of the questions being asked is if they would recommend the studio to a friend. The studio has given the survey to a simple random sample of 65 clients during the past two weeks. If the true proportion of clients who are very satisfied with the Big Smiles Portrait Studio and would therefore recommend the studio to a friend is 82%, what is the probability that more than 60 clients in the sample would answer Yes on the survey question? Select one: a. 0.0119 b. 0.0054 c. 0.0264 d. 0.9231

The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past few years. It is estimated that approximately 90% of students now own a cell phone. Fifteen students are to be selected at random from a large university. Assume that the proportion of students who own a cell phone at this university is the same as nationwide. Let X = the number of students in the sample of 15 who own a cell phone. Reference: Ref 5-21 What is the appropriate distribution for X? Select one: a. X is N(15, 0.9) b. X is B(15, 0.9) c. X is B(15, 13.5) d. X is N(13.5, 1.16)

There are twenty multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth 5 points and only one response per question is correct. Suppose a student guesses the answer to each question, and her guesses from question to question are independent. If the student needs at least 40 points to pass the test, the probability the student passes is closest to Select one: a. 0.0609. b. 0.1019. c. 0.9590.

When a particular penny is held on its edge and spun, the probability that heads are face up when the coin comes to rest is 4/9. If the coin is spun 4 times, the probability that the coin will come up heads exactly twice is (assume trials are independent) Select one: a. 16/81. b. 0.366. c. 0.061.

Which of these settings does NOT allow use of a matched pairs t procedure? Select one: a. You interview both the husband and the wife in 64 married couples and ask each person about their ideal number of children. b. You interview a sample of 64 unmarried male students and another sample of 64 unmarried female students and ask each about their ideal number of children. c. You interview 64 female students in their freshman year and again in their senior year and ask each about their ideal number of children. d. You interview 64 female students and their mothers and ask each about their ideal number of children.

Two researchers, Wiebe and Bortolotti, in 2002 examined the color in tail feathers of Northern Flickers. It sometimes occurs that these birds have one tail feather, which differed from the rest in terms of its color. This was perhaps because the feather had re-grown after having been lost. The "odd" feather and a "typical" feather from each of the selected birds were analyzed with respect to the degree of "yellowness." Larger values of the measurement indicate the feather color is less yellow. The question they wished to address was whether or not "odd" feathers and the "typical" feathers differed with respect to the yellowness of their color. Bird A B C D E F Odd Feather 324 245 299 198 27 45 Typical Feather 255 213 190 185 45 25 If you use the 0.05 level of significance, what conclusion would you reach? Select one or more: a. There is sufficient evidence to conclude the mean yellowness of the two types of feathers are different. b. There is insufficient evidence to conclude the mean yellowness of the two types of feathers are different. c. There is sufficient evidence to conclude the mean yellowness of the two types of feathers are the same. d. There is insufficient evidence to conclude the mean yellowness of the two types of feathers are the same.

B and D

A small New England college has a total of 400 students. The Math SAT is required for admission, and the mean score of all 400 students is 640. The population standard deviation is known to be 60. The formula for a 95% confidence interval yields the interval 640 ± 5.88. Determine which of the following statements is (are) FALSE. Select one or more: a. If we repeated this procedure many, many times, only 5% of the 95% confidence intervals would fail to include the mean Math SAT score of the population of all students at this college. b. The probability that the population mean will fall between 634.12 and 645.88 is 0.95. c. The interval is incorrect. It is much too narrow. d. If we repeated this procedure many, many times, the sample mean would fall between 634.12 and 645.88 about 95% of the time.

B, C, and D

A coin is about to be tossed multiple times. Assume the coin is fair, i.e., the probability of heads and the probability of tails are both 0.5. Reference: Ref 5-24 If the coin is tossed six times, what is the probability that less than ⅓ of the tosses are heads? Select one: a. 0.0049 b. 0.094 c. 0.109 d. 0.344

A fisheries biologist has been studying horseshoe crabs using categorical variables, but she has decided that reporting the data as continuous variables would be more useful. She has sampled 100 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). The proposed regression equation is weighti = β0 + β1 × widthi + εi, where the deviations εi are assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software. Variable Estimate Std. error of estimate Constant 2.3013 0.9788 Width 0.7963 0.0939 R2 = 0.423, s = 2.2018 Reference: Ref 23-1 Which of the following conclusions seems most justified? Select one: a. There is no evidence of a relationship between the widths and weights of horseshoe crabs. b. There is distinct evidence (P-value less than 0.05) that there is a negative correlation between widths and weights of horseshoe crabs. c. There is fairly strong evidence of a strong, positive, linear relationship between widths and weights of horseshoe crabs. d. The presence of strongly influential observations in these data makes it impossible to draw any conclusions about the relationship between widths and weights of horseshoe crabs.

A large fishing farm with thousands of fish has been treating its fish to stop a spreading fungal infection. The owners want to know if more than 10% of the fish population is infected (more than 10% is not considered "contained"). A random sample of 50 fish is taken, and a careful examination determines that 6 of the fish sampled are infected. Obtain the P-value for the appropriate test. Using a significance level of 0.05, you Select one: a. can conclude that the infection is contained. b. can conclude that the infection is not contained. c. fail to reach a conclusion as to whether or not the infection is contained. d. can conclude that the population proportion of infected fish is 10%.

A medical research team is interested in determining whether a new drug has an effect on creatine kinase (CK), which is often assayed in blood tests as an indicator of myocardial infarction. A random selection of 20 patients from a pool of possible subjects is selected, and each subject is given the medication. The subjects' CK levels are observed initially, after three (3) weeks, and again after six (6) weeks. The purpose is to study the CK levels over time. Here is a summary of the findings: Time (weeks) Mean CK level (U/L) Standard deviation (U/L) 0 121 20.37 3 106 16.09 6 100 10.21 In this example, we notice that Select one: a. the data show very strong evidence of a violation of the assumption that the three populations have the same standard deviation. b. ANOVA cannot be used on these data because the sample sizes are much too small. c. the assumption that the data are independent for the three time points is unreasonable because the same subjects were observed each time. d. there is no reason not to use ANOVA in this situation.

A newspaper is conducting a statewide survey concerning the race for governor. The newspaper will take a simple random sample of n registered voters and determine X = the number of voters that will vote for the Democratic candidate. Is there evidence that a clear majority of the population will vote for the Democratic candidate? To answer this, they will test the hypotheses H0: p = 0.50 versus Ha: p > 0.50. Reference: Ref 8-8 Consider the two scenarios where in Scenario 1, n = 1200 and X= 640. In Scenario 2, n = 120 and X = 64. Even though the values for are the same in the two scenarios, we come to opposite decisions (we reject H0 in one scenario and we do not in the other). What is the reason for these contrasting decisions? Select one: a. When the sample size is larger, the margin of error is larger. This may cause the results to be biased. b. The 64 people in the small sample must also be part of the 640 people in the big sample. This means we are counting them twice, causing the results of the test with the larger sample to be wrong. c. The sample size in the first scenario is much larger, leading to a test with higher power. d. We must have made a mistake. With equal values of , we must come to equal decisions.

A random sample of 140 births from local records showed this distribution across days of the week:DaySunMonTueWedThursFriSatBirths13232420271815Here are the results of an analysis of this data to examine if the distribution is uniform:Which of the following is correct? Select one: a. The test is invalid because several weeks of data were collected. b. The test is valid because all observed counts are greater than 1. c. Multiple-births (e.g., twins) need to be excluded from the study.

A study of the effects of sedating and non-sedating antihistamines on driving impairment was done in a driving simulator. Volunteers were randomly assigned to take either a sedating antihistamine, a non-sedating antihistamine, or a placebo. Their steering instability in the simulator was recorded on a quantitative scale. To analyze these data, you would use Select one: a. a z test. b. a t test. c. an ANOVA F test. d. a chi-square test.

A study was conducted to explore the relation between alcohol consumption and hypertension. 7400 nurses were surveyed and information about the amount of alcohol consumed per day (on average) and whether or not they suffered from hypertension was collected. The following table summarizes the information that was obtained. Assuming the nurses surveyed were a simple random sample from the population of all nurses in the United States, the appropriate null hypothesis for these data is Select one: a. the distribution of the average number of alcoholic drinks per day is the same for the population of nurses with hypertension and for the population of nurses who do not have hypertension. b. the distribution of the presence of hypertension in nurses is the same for the populations of nurses who do not drink, nurses who drink 0.01 - 1.00 alcoholic drinks on average per day, nurses who drink 1.01 - 2.00 alcoholic drinks on average per day, and nurses who drink more than 2 alcoholic drinks on average per day. c. the presence or absence of hypertension in nurses is independent of whether they do not drink, drink 0.01 - 1.00 alcoholic drinks on average per day, drink 1.01 - 2.00 alcoholic drinks on average per day, or drink more than 2 alcoholic drinks on average per day.

Blood pressure tends to increase with weight. A sample of 14 male employees who worked at a local business had their systolic blood pressure measured (mm Hg) along with their body mass (kg). Here is some information about the fit of the linear model:Which of the following is correct? Select one or more: a. Ninety-five percent of men have blood pressure between 1.14 and 2.17 mm. b. The youngest man had a blood pressure of 6.38. c. The estimated increase in blood pressure for each additional kilogram of mass is between about 1.13 mm and 2.17 mm. d. The estimated increase in blood pressure for the heaviest man is less than about 45.2 mm for each additional kilogram of mass.

Blood pressure tends to increase with weight. A sample of 14 male employees who worked at a local business had their systolic blood pressure measured (mm Hg) along with their body mass (kg). Here is some information about the fit of the linear model:Which of the following is correct? Select one or more: a. The mean blood pressure is about 33.85. b. The correlation between blood pressure and body mass is about 0.43. c. The standard deviation about the regression line is about 33.8 mm. d. The margin of error is about 33.8 mm.

Chronic fatigue syndrome (CFS) is a debilitating disease of unknown etiology that is estimated to affect 17 million people worldwide. In a case-control observational study, researchers identified DNA from a human gammaretrovirus (XMRV) in 68 of 101 CFS patients (67%) compared with 8 of 218 (3.7%) healthy controls. Do the data show evidence of a relationship between XMRV and CFS? Reference: Ref 22-8 Using significance level of 5%, you conclude Select one: a. that there is significant evidence that XMRV causes CFS in a large fraction of the CFS patients. b. that the data are consistent with the null hypothesis of no relationship between XMRV and CFS. c. that there is significant evidence of a relationship between XMRV and CFS, and XMRV is much more frequent among CFS patients than would be expected if there was no such relationship. d. nothing, because the test assumptions are not met.

Ginger root is used by many as a dietary supplement. A manufacturer of supplements produces capsules that are advertised to contain at least 500 mg. of ground ginger root. A consumer advocacy group doubts this claim and tests the hypotheses H0 μ: = 500 Ha: μ < 500 They take a random sample of 100 ginger root capsules produced by the manufacturer and compute the test statistic where is the mean amount of ginger root in the 100 capsules sampled. Based on other information, the advocacy group knows the value of . If the test statistic z has value 2.39, we may conclude that Select one or more: a. we reject H0 at level α = 0.05 but not at level α = 0.01. b. we reject H0 at level α = 0.01. c. we do not reject H0 at level α = 0.05.

In a study on scholastic test scores of entering college freshmen, a random sample of colleges across the nation is selected and the average SAT Math score for the freshman class is recorded. The colleges are categorized according to their affiliation: Public, Private, or Church. Does it appear that freshmen entering the three different types of schools do equally well on the SAT Math? Computer output is included below: Source Sum of squares DF Mean square F P-value Groups 63906.2 2 31953.1 5.696 0.005 Error 353440.2 63 5610.2 Total 417346.4 65 Reference: Ref 12-4 At a significance level of 0.05, what is the appropriate conclusion about the average SAT Math scores? Select one: a. The average SAT Math scores for freshmen attending colleges with the three different affiliations appear to be the same. b. Each of the three average SAT Math scores for freshmen attending colleges with the three different affiliations appear to be different. c. It appears that freshmen attending at least one of the three different types of college have a different average SAT Math score. d. Freshmen at one type of affiliated college have a significantly better average SAT Math score than the other two.

In the race for mayor of Columbus, Ohio, in 1999, one poll found that 61.1% of those surveyed would vote for the Democratic candidate. The poll had a 4.1% margin of error with 95% confidence. We may correctly conclude that Select one: a. there is a 95% probability that the Democratic candidate will receive the majority of the vote because the interval does not include 50%. b. if the poll were repeated many times and a 95% confidence interval computed for each, approximately 95% of these would show the Democratic candidate to have the majority of the vote. c. if the poll were repeated many times and a 95% confidence interval computed for each, approximately 95% of these would include the true percentage of the population that would vote for the Democratic candidate.

Mice populations rise and fall with the abundance of acorns, their favored food. Experimenters studied two similar forest areas in a year when the acorn crop failed. They added hundreds of thousands of acorns to one area to imitate an abundant acorn crop, while leaving the other area untouched. The next spring, 54 of the 72 mice trapped in the first area were in breeding condition, versus 10 of the 17 mice trapped in the second area. The p-value for comparing the proportion of breeders in the two areas was 0.18. Which of the following is correct? Select one: a. There is an 18% chance that the breeding rate is the same in both areas. b. There is an 18% chance that the breeding rate is different in the two areas. c. If the breeding rates were the same, there is an 18% chance of seeing this difference in breeding rates (or more extreme). d. If the breeding rates were different, there is an 18% chance of seeing this difference in the breeding rates (or more extreme).

Simple random samples of 350 women and 450 men from Michigan are obtained. The 800 people in the sample are categorized according to where they went to school: in-state, out-of-state, or no college. Location Gender In-state Out-of-state No college Total Male 166 205 79 450 Female 154 115 81 350 Total 320 320 160 800 The SPSS output for the above table is given below. The output includes the cell counts and most expected cell counts. Expected counts are printed below observed counts: Reference: Ref 9-9 What would be the null hypothesis for a chi-square test based on these data? Select one: a. College location and gender are dependent. b. The average college location is the same for men and women. c. The distribution of college location is the same for men and women. d. The distribution of gender is different for the three different college locations.

The Big Smiles Portrait Studio is conducting a survey among their clients. One of the questions being asked is if they would recommend the studio to a friend. The studio has given the survey to a simple random sample of 65 clients during the past two weeks. Reference: Ref 5-29 If the true proportion of clients who are very satisfied with the Big Smiles Portrait Studio and would therefore recommend the studio to a friend is 82%, how many clients in the sample would we expect to answer Yes on the survey question? Select one: a. 0.82 b. 53 c. 53.3 d. 54

The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past few years. It is estimated that approximately 90% of students now own a cell phone. Fifteen students are to be selected at random from a large university. Assume that the proportion of students who own a cell phone at this university is the same as nationwide. Let X = the number of students in the sample of 15 who own a cell phone. Reference: Ref 5-21 On average, how many students will own a cell phone in a simple random sample of 15 students? Select one: a. 9 b. 13 c. 13.5 d. 14

The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past few years. It is estimated that approximately 90% of students now own a cell phone. Fifteen students are to be selected at random from a large university. Assume that the proportion of students who own a cell phone at this university is the same as nationwide. Let X = the number of students in the sample of 15 who own a cell phone. Reference: Ref 5-21 What is the probability that all students in a simple random sample of 15 students own a cell phone? Select one: a. 0 b. 0.1 c. 0.206

The proportion of students who own a cell phone on college campuses across the country has increased tremendously over the past few years. It is estimated that approximately 90% of students now own a cell phone. Fifteen students are to be selected at random from a large university. Assume that the proportion of students who own a cell phone at this university is the same as nationwide. Let X = the number of students in the sample of 15 who own a cell phone. Reference: Ref 5-21 What is the standard deviation of the number of students who own a cell phone in a simple random sample of 15 students? Select one: a. 0.077 b. 0.09 c. 1.16 d. 1.35

We want to see if a panel of 30 expert wine testers can distinguish between a 1990 and 1991 Chardonnay. We present them each with three glasses of wine. The three glasses are either two glasses of the 1990 and one glass of the 1991 in a random order, or two glasses of the 1991 and one glass of the 1990 in a random order. The experts are supposed to identify which of the three glasses contains a different wine. If each of the 30 experts is just guessing and X is the number that guess correctly, then the sample proportion = X /30 who guess correctly has Select one: a. = .0056 b. = 0063 c. = .0861

We wish to test the null hypothesis that the proportion of subsequent infestations is the same, regardless of the treatment assigned. Which of the following statements is true? Select one: a. We cannot test this hypothesis because the forester did not record the expected counts. b. The test of the null hypothesis will have a very small P-value (below 0.0001) because the counts in each row are not identical. c. We cannot test this hypothesis because the expected cell counts are less than 5 in too many of the cells. d. The test of the null hypothesis will have a very small P-value (below 0.0001) because there were so few cases where there was more than one recurring infestation.

Which of the following might be reasonably modeled by the binomial distribution? Select one: a. The number of customers that enter a store in a one-hour period, assuming customers enter independently. b. The number of questions you get correct on a 100-question multiple choice exam in which each question has only four possible answers. Assume you have studied extensively for the test. c. Neither choice is correct.

A production process, when functioning as it should, will still produce 2% defective items. A random sample of 10 items is to be selected from the 1000 items produced in a particular production run. Let X be the count of the number of defective items found in the random sample. What can be said about the variable X? Select one: a. We can use a Normal distribution with a mean of 20 and a standard deviation of 4.43 as an approximation for the distribution of X. b. X is approximately Normal with μ = 10 and σ = 0.44. c. X has an approximate binomial distribution with parameters 1000 and 0.01. d. X has an approximate binomial distribution with a mean of 0.2 and a standard deviation of 0.443. e. Without additional information we are unable to determine if X is approximately Normally distributed or if it has a binomial distribution.

An airplane has a front and a rear door, both of which are opened to allow passengers to exit when the plane lands. The plane has 100 passengers aboard. Let X = the number of passengers exiting through the front door. What is the appropriate distribution for the random variable X? Select one: a. A binomial distribution with mean 50. b. A binomial distribution with n = 100 trials but success probability not equal to 0.5. c. A Normal distribution with a standard deviation of 5. d. None of the above.

An inspector inspects a shipment of medications to determine the efficacy in terms of the proportion p in the shipment that failed to retain full potency after 60 days of production. Unless there is clear evidence that this proportion is less than 0.05, she will reject the shipment. To reach a decision, she will test the following hypotheses using the large-sample test for a population proportion: H0 : p = 0.05, Ha : p < 0.05 To do so, she selects an SRS of 200 pills. Suppose that eight of the pills have failed to retain their full potency. Reference: Ref 19-6 Which of the following assumptions for inference about a proportion using a hypothesis test are violated? Select one: a. The data are an SRS from the population of interest. b. The population is at least 20 times as large as the sample. c. n is so large that both np0 and n(1- p0) are 10 or more, where p0 is the proportion with major defects if the null hypothesis is true. d. There appear to be no violations.

Are different species of mosquitoes attracted differently to the two sexes? A study was conducted where three closely related species of mosquitoes were presented with an arm from a male or a female and the selection was recorded. Here is the two-way table of counts: FemaleMaleSpecies A24866Species B514105Species C351225The results of the statistical test for the preceding table are:TestChiSquareProb>ChiSqPearson80.874<.0001*Your conclusion is: Select one: a. There is no evidence of a relationship between the species of mosquito and the sex of the arm. b. There is evidence that mosquitoes target women. c. There is evidence that the numbers of the three species that prefer female arms is different. d. There is evidence that the three species differ in their preferences for the two types of arms.

For which of the following does the random variable X have a binomial distribution? Select one: a. X is the number of pastrami sandwiches sold at a deli in a month. b. X is the number of speeding tickets given out at a randomly picked location in a city during a calendar year. c. X is the number of defects found in 100 meters of fiber optic cable. d. X is the number of people in a random sample of size 50 from a large population that have type-AB blood. e. X is the number of tries a kicker makes to score four field goals in a football game.

Given that a goodness of fit test has the null hypothesis rejected, the next step in investigating the distribution is Select one: a. to compare observed and expected percents. b. to compare observed and expected cell counts. c. to look at the larger components of the chi-square statistic. d. All of the above

If the null hypothesis is true, the ANOVA table shows that the P-value is 0.5383. What should we conclude from this? Select one: a. The mean of Chemical D is certainly different from the mean of Chemical A. b. Some of the chemicals have a different effect on the brightness of the paper. c. The null hypothesis should be rejected in favor of the alternative hypothesis. d. Caution should be exercised on any conclusion from the ANOVA because the assumption of equal standard deviation among chemicals may be suspect. e. With only 19 degrees of freedom for Total, nothing much can be concluded from this experiment.

Mr. Aaron is about to interview four candidates for a certain job. He hopes all the candidates turn off their cell phones, because he does not like to be interrupted by a ringing cell phone. If there is only one candidate whose cell phone rings during the interview, Mr. Aaron will immediately not hire this candidate. If there is only one candidate whose cell phone does not ring during the interview, he will immediately hire this candidate. Suppose all four candidates own cell phones and none turn his/her cell phone off. Each of the candidates will have a 50% chance of being called during their interview. What is the probability that Mr. Aaron will find himself in either one of the two above-described situations: to immediately not hire one candidate because his/her cell phone rang during the interview or to immediately hire one candidate because his/her cell phone was the only one that did not ring during the interview? Select one: a. 0.0625 b. 0.125 c. 0.25 d. 0.50

One possible effect of air pollution is genetic damage. A study exposed a group of mice to air near a steel mill and another group of mice to air in a rural area to see if the mutation rate was higher for mice exposed to steel mill air. The number of mice that had mutations in their offspring was recorded: No MutationMutation presentRural15023Steel Mill6630The chi-square test statistic was 12.6. Which of the following is correct? Select one: a. The z test statistic is 158.8. b. Because the p-value is 12.6%, there is no evidence against the hypothesis. c. This chi-square value is compared to a chi-square distribution with 4 degrees of freedom. d. There is strong evidence against the hypothesis of no association.

Some chronic conditions produce episodes of severe flare-ups ("active" stage) between healthy periods ("inactive" stage). The active stage often necessitates immediate medical treatment. Researchers looked for biomarkers that might help identify these active stages. Here are data on the relative abundance of the protein BPG0199 in two independent random samples of men with the same chronic condition, 7 in the active phase and 9 in the inactive phase. Active Inactive 2.6 1.2 2.7 2.1 2.0 1.8 2.4 1.5 1.9 1.9 1.4 3.2 1.8 1.3 1.9 1.6 We want to know if there is a significant difference in the relative abundance of the protein BPG0199 between men in the active stage and men in the inactive phase and, therefore, we test the following hypotheses: H0 : μA = μI , Ha : μA ≠ μI Reference: Ref 18-9 The test degrees of freedom are roughly 13. The P-value for the test is closest to Select one: a. 0.001. b. 0.03. c. 0.1. d. 0.3.

Television networks frequently run public opinion polls on issues of concern. Recently one network conducted a scientific poll asking a question concerning the approval rating of the way President Obama was handling the Iraq War. At about the same time a second network ran an online poll using a very similar question. The results of the two polls are summarized in the following table: Poll Scientific Online Approve 339 385 Disapprove 780 573 Total 1119 958 We would like to test to see if the two polls are consistent with respect to the proportion who Approve of President Obama's handling of the war, i.e., H0: Reference: Ref 9-5 A statistic was calculated under the null hypothesis, which has the value 22.28. If the respondents in both polls can be considered to come from random samples, what is this statistic? Select one: a. It is approximately a t with 1 degree of freedom. b. It is a statistic with approximately a chi-square distribution with 3 degrees of freedom. c. It is a statistic with an approximate chi-square distribution with 2 degree of freedom. d. It is a z statistic. e. It is none of the above.

The Big Smiles Portrait Studio is conducting a survey among their clients. One of the questions being asked is if they would recommend the studio to a friend. The studio has given the survey to a simple random sample of 65 clients during the past two weeks. Reference: Ref 5-29 Big Smiles has studios all across the country. Each studio surveys 65 of their clients and records the number of surveyed clients that respond Yes. If a studio scores in the top 6% of the distribution for the number of clients who answer Yes, then the studio will receive an award. Approximately how many clients had to answer Yes on the survey question before the studio will win an award? Select one: a. 48 b. 48.5 c. 57 d. 58

The Sleep Heart Health Study enrolled a randomly selected cohort of 6294 adults not treated for sleep-disordered breathing. The men and women in the study were classified into four groups depending on the extent of their sleep-disordered breathing (none, mild, moderate, or severe). Is there significant evidence that men and women differ in extent of their sleep-disordered breathing? Here is an incomplete Minitab output to help you answer this question.Chi-Square Test:Expected counts are printed below observed countsChi-Square contributions are printed below expected counts none mild moderate severe Totalwomen 2167 821 265 99 3352 1826.18 957.03 387.18 63.605 19.335 38.555 men 1262 976 462 242 2942 1602.82 839.97 339.82 72.469 22.029 43.928 Total 3429 1797 727 341 6294 Reference: Ref 22-1 Based on the Minitab output and your calculations, you can conclude that Select one: a. there is not enough evidence (P > 0.05) to conclude that there is an association between the severity of sleep-disordered breathing and sex. b. there is no association between the severity of sleep-disordered breathing and sex (P < 0.05). c. there is a significant (P < 0.05) association between the severity of sleep-disordered breathing and sex, and severe cases tend to be more common in women than in men. d. there is a significant (P < 0.05) association between the severity of sleep-disordered breathing and sex, and severe cases tend to be more common in men than in women.

The length of time it takes to get through the security checks at a very large urban airport is a random variable with mean μ = 20.6 minutes and standard deviation σ = 8.4 minutes. A simple random sample of 36 airline passengers is to be observed going through security. Reference: Ref 5-6 What is the variance, , of the sampling distribution of the sample mean, ? Select one: a. 8.4 minutes b. 20.6 minutes c. 1.4 minute d. None of the above. e. Close to 8.4 minutes but we can't be certain without having the data to determine it.

The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with standard deviation σ =0.05 grams per mile (g/mi). A random sample of 12 cars of this particular model is taken and is found to have a mean NOX emission of = 0.298 g/mi. Government regulations call for NOX emissions no higher than 0.3 g/mi. Do the data provide evidence that this particular meets the government regulation? Reference: Ref 14-10 You conclude from these data that Select one: a. the null hypothesis is proved at significance level 5%. b. the alternative hypothesis is proved at significance level 5%. c. there is evidence supporting the alternative hypothesis at significance level 5%. d. there is not enough evidence to reject the null hypothesis at significance level 5%.

Twenty-five patients at a large clinic volunteer to participate in a study regarding weight loss. These 25 patients had a mean weight loss score of 4500 g over two weeks. Suppose we know that the standard deviation of the population of weight changes on this particular diet is 100 g. Assuming the population of weight losses is Normally distributed, a 90% confidence interval for the mean weight loss μ for the population, based on the collected data, is Select one: a. 4500 ± 32.9. b. 4500 ± 39.2. c. 4500 ± 164.5. d. not trustworthy.

What conclusion might one draw by looking at the side-by-side boxplots? Select one: a. The ANOVA assumption of Normality of the data is satisfied. b. The population means certainly are different. c. There is insufficient data to justify reaching any conclusion here. d. There is different variability from brand-to-brand but not enough difference to raise concern about the common variance ANOVA assumption. e. The consumer group should look at the Normal quantile plot to verify the common variance assumption.

Which of the following is not a requirement for using the matched-pairs t procedure? Select one: a. Subjects/experimental units are the same or similar. b. Data are the difference between two measurements. c. One sample t procedures are applied to the differences of the two measurements/observations. d. Measurements are taken on completely independent subjects.

You randomly select two fish from a lake and measure their length. Let X be the sum of the lengths of the two fish. The distribution of the lengths of all the fish in the lake is the Select one: a. sampling distribution of the average lengths. b. sampling distribution of the proportion. c. Normal distribution of fish lengths. d. population distribution of fish lengths.

Let X be a random variable, which has a binomial distribution with a mean of μ = 8 and a standard deviation of σ = 2.19. The parameters n and p for this binomial distribution are respectively: Select one: a. n = 16, p = 0.5. b. n = 13.3, p = 0.6. c. n = 10, p = 0.8. d. n = 20, p = 0.6. e. n = 20, p = 0.4.

When engaging in weight control (fitness/fat burning) types of exercise, a person is expected to attain about 60% of their maximum heart rate. For 20-year-olds, this rate is approximately 120 bpm. A simple random sample of 100 20-year-olds was taken, and the sample mean was found to be 107 bpm with a standard deviation of 45 bpm. Researchers wonder if this is evidence to conclude that the expected level is actually lower than 120 bpm. To determine this, we test the following hypotheses: H0 : μ= 120, Ha : μ< 120 Suppose the mean and standard deviation obtained were based on a sample of size 25 rather than 100. The P-value would be Select one: a. larger. b. smaller. c. unchanged because the difference between and the hypothesized value μ = 120 is unchanged. d. unchanged because the variability measured by the standard deviation stays the same. e. Cannot be determined

A study was conducted to determine if there was a difference in the driving ability of students from West University and East University by sending a survey to a sample of 100 students at both universities. Of the 100 sampled from West University, 15 reported they had been involved in a car accident within the past year. Of the 100 randomly sampled students from East University, 12 students reported they had been involved in a car accident within the past year. Reference: Ref 8-30 The confidence interval computed to estimate the difference in the proportion of students between the two universities who had been involved in a car accident will take into account the variability that exists due to nonresponse errors and students misinterpretation of the question. Select one: True False

False

The analysis of variance can be used to test for differences between population means when there are only two populations. Select one: True False

True

The binomial distribution can be used to model situations where there is/are ____ outcomes.

two

Suppose we were interested in determining if there were differences in the average prices among two local supermarkets. We randomly pick six items to compare at both supermarkets. Which statistical procedure would be best to use for this study? Select one: a. Matched-pairs t procedure. b. One-sample t test. c. Two-sample t test. d. None of the above.

A simple random sample of 100 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago. The sample mean was 7 years with a standard deviation of 2 years. Assume the distribution of the time the employees have worked for the postal service is approximately Normal. The hypotheses being tested are H0: μ = 7.5, Ha: μ ≠ 7.5. Suppose the mean and standard deviation obtained were based on a sample of size n = 25 postal workers rather than 100. What do we know about the value of the P-value? Select one: a. It would be larger. b. It would be smaller. c. It would be unchanged because the difference between and the hypothesized value μ = 7.5 is unchanged. d. It would be unchanged because the variability measured by the standard deviation stays the same.

A sprinkler system is being installed in a newly renovated building on campus. The average activation time is supposed to be at most 20 seconds. A series of 12 fire alarm/sprinkler system tests results in an average activation time of 21.5 seconds. Do these data indicate that the design specifications have not been met? The hypotheses to be tested are H0: μ = 20 versus Ha: μ > 20, where μ = the true average activation time of the sprinkler system. Assume that activation times for this system are Normally distributed with σ = 3 seconds. The data is found to be statistically significant at the 5% significance level. What does this mean with respect to the question "Do these data indicate that the design specifications have not been met?" Select one: a. The decision means that we rejected the null hypothesis. We can therefore conclude that the design specifications do not seem to have been met. b. The decision means that we failed to reject the null hypothesis. We can therefore conclude that the design specifications do not seem to have been met. c. The decision means that we rejected the null hypothesis. We can therefore conclude that the design specifications seem to have been met. d. The decision means that we failed to reject the null hypothesis. We can therefore conclude that the design specifications seem to have been met.

All else being equal, which of the following is true? Select one: a. As you increase the sample size, you will decrease the p-value. b. As you increase the standard deviation, the level will increase. c. As you increase the level, the p-value decreases. d. As the sample mean gets farther from the mean, the p-value will increase.

Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds. Over time, the lengths of the flowers and the forms of the hummingbirds' beaks have evolved to match each other. The following is an analysis of the length (mm) of the two color varieties:Which of the following is correct? Select one: a. The estimated difference in mean length between the two varieties is 3.53 (SE 0.45) mm. Because the confidence interval does not contain 0, there is evidence of a difference in mean length. This is correct. Text reference: Section 18.3 Two-sample t Procedures b. About 95% of flowers have a difference in lengths between 2.6 and 4.4 mm. c. The dot-plot shows several outliers. Consequently, the t procedure is invalid. d. The degrees of freedom are fractions but the t table shows that they are integers. An error must have been made in computing the degrees of freedom.

I use computer software to do the following. I generate ten random numbers from a N(500, 100) distribution. From these ten numbers I compute a 95% confidence interval for the mean using the formula where is the mean of the ten random numbers. I then repeat this process (generating a new set of 10 random numbers from a N(500, 100) distribution each time) until I have produced 1000 such intervals. Which of the following will be true? Select one or more: a. Approximately 95% of the intervals will contain the value 500. b. Approximately 95% of the intervals will contain the value 100. c. Approximately 97.5% of the intervals will contain the true mean because the probability that a standard Normal random variable is less than 1.96 is 0.975. I have incorrectly used the formula for a 97.5% confidence interval.

It has been claimed that women live longer than men; however, men tend to be older than their wives. Ages of sixteen husbands and wives from England were obtained. The null hypothesis of equality of means is rejected. What conclusion can be made from this study (assuming normality requirements are met)? Select one: a. English husbands are older than their wives. This is correct. The sample was drawn only from English couples, so only pertains to them.Text reference: section 7.1. b. Husbands are older than their wives. c. The sample was too small. No conclusions can be made.

Researchers fed cockroaches a sugar solution. Ten hours later, they dissected the cockroaches and measured the amount of sugar in various tissues. Here are the amounts (in micrograms) of d-glucose in the hindguts of 5 cockroaches:55.95 68.24 52.73 21.50 23.78 The method used to compute this confidence interval has a 95% probability of producing an interval that captures Select one: a. the mean amount of d-glucose in hindguts μ for the population of all lab cockroaches fed a similar sugar solution. b. the mean amount of d-glucose in hindguts for a single random sample of 5 lab cockroaches fed a similar sugar solution. c. the mean amount of d-glucose in hindguts for any random sample of 5 lab cockroaches fed a similar sugar solution. d. the amount of d-glucose in hindguts x for a randomly selected lab cockroach fed a similar sugar solution.

Some chronic conditions produce episodes of severe flare-ups ("active" stage) between healthy periods ("inactive" stage). The active stage often necessitates immediate medical treatment. Researchers looked for biomarkers that might help identify these active stages. Here are data on the relative abundance of the protein BPG0235 in two independent random samples of men with the same chronic condition, 7 in the active phase and 9 in the inactive phase. Active Inactive 1.0 1.1 1.0 0.9 1.0 0.5 1.2 0.9 1.2 1.0 1.3 1.0 1.0 0.8 0.7 1.1 We want to know if there is a significant difference in the relative abundance of the protein BPG0235 between men in the active stage and men in the inactive phase and, therefore, we test the following hypotheses: H0 : μA = μI , Ha : μA ≠ μI Reference: Ref 18-8 What assumption must be true for this test result to be correct? Select one: a. The population distributions must be roughly Normal. b. The sample standard deviations must be similar. c. The population standard deviations must be equal. d. The same individuals must be measured during an active phase and during an inactive phase.

The P-value of a test of the null hypothesis is Select one: a. the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed. b. the probability, assuming the null hypothesis is false, that the test statistic will take a value at least as extreme as that actually observed. c. the probability the null hypothesis is true. d. the probability the null hypothesis is false.

The fact that, as the sample size increases, the distribution of the sample proportion becomes more Normal is due to the Select one: a. central limit theorem. b. unbiasedness of the sample proportion. c. fact that n is in the denominator of the sample proportion. d. law of large numbers.

The lengths of individual male fish in a pond have a very skewed distribution with a mean of 18.6 cm and a standard deviation of 6.0 cm. There are many small fish and a few very large fish. A sample of 10 fish is taken using a trap that is equally effective for all lengths of fish. Which of the following is correct? Select one: a. The sample mean will remain an unbiased estimate of the population mean despite the skewness. This is correct. The mean of the sampling distribution of xbar is always mu. This doesn't depend on whether the population is normally distributed or the sample size is large. b. The sampling distribution of the sample mean will be exactly Normally distributed. c. The standard deviation of the sample mean will be larger than the standard deviation of the individual lengths. d. The distribution of the individual lengths is approximately Normally distributed.

The level of calcium in the blood of healthy young adults follows a Normal distribution with standard deviation of 0.4. A clinic measures the blood calcium of 100 healthy pregnant young women at their first visit for prenatal care. The mean of these 100 measurements is 9.8. Is this evidence that the mean calcium level in the population of healthy pregnant young women is less than 10? Determine which of the following statements is (are) true. Select one or more: a. H0 should be rejected. b. H0 should not be rejected. c. Ha should be rejected. d. There is a 5% chance that the null hypothesis is true.

The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with standard deviation σ = 0.05 grams per mile (g/mi). Government regulations call for NOX emissions no higher than 0.3 g/mi. In testing H0 : μ = 0.3 versus Ha : μ < 0.3 using significance level 0.05, we find that the power of this test against an alternative of μ = 0.28 based on a random sample of size n = 40 is 0.808. Reference: Ref 15-5 Using a larger sample size (n = 50) would Select one: a. increase the power of this particular test. b. decrease the power of this particular test. c. increase the probability of a Type I error. d. decrease the probability of a Type I error.

The physician-recommended dosage of a new medication is 14 mg. Actual administered doses vary slightly from dose to dose and are Normally distributed with mean μ standard deviation .3. A representative of a medical review board wishes to see if there is any evidence that the mean dosage is more than recommended and so intends to test the hypotheses given below. H0 : μ =14, Ha : μ >14 To do this, he selects 16 doses at random and determines the weight of each. He finds the mean to be 14.12 mg and the standard deviation to be 0.24 mg. Based on these data, Select one: a. a Z-test should be used. Population is normal and population standard deviation is known. b. a T-test should be used. c. neither should be used.

The variability of a statistic is described by Select one: a. the spread of its sampling distribution. b. the amount of bias present. c. the vagueness in the wording of the question used to collect the sample data. d. the stability of the population it describes.

Determine whether each of the following statements regarding this density curve is true or false. It is symmetric. The total area under the curve is 1. The median is 1. The mean is 1.

All are true

A 95% confidence interval for the true mean cholesterol of adult males based on 25 randomly selected subjects extends from 175 mg/L to 250 mg/L. A proper interpretation of the confidence interval would be that Select one: a. 95% of the population has a cholesterol level between 175 and 250 mg/L. b. we are 95% confident that the true mean cholesterol level of the population falls between 175 and 250 mg/L. c. there is a 95% chance that a randomly selected individual has a cholesterol level that falls between 175 and 250 mg/L. d. in repeated samples of size 25, the sample mean will fall between 175 and 250 mg/L 95% of the time.

A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons. Reference: Ref 5-8 If a simple random sample of four tanks is selected, and their capacities can be considered independent, what is the probability that all four will hold between 14.75 and 15.10 gallons of gas? 0.2397 b. 0.6808 c. 0.9084 d. 2.7988

A level α two-sided significance test rejects the null hypothesis H0 :μ = μ0 exactly when Select one: a. the z test statistic differs from μ0. b. the value μ0 falls outside a level 1 - α confidence interval for μ. c. the z test statistic differs from μ. d. the value μ falls outside a level 1 - α confidence interval for μ0.

A market research company wishes to find out whether the population of students at a university prefers Brand A or Brand B of instant coffee. A random sample of 100 students is selected, and each one is asked to try Brand A and then Brand B (in random order). They then indicate which brand they prefer, and 65 students preferred Brand B. Which is the parameter of interest? Select one: a. the proportion of sampled students who preferred Brand B b. the proportion of all students who prefer Brand B c. the proportion of all students who were sampled d. the proportion of students who tasted Brand A first

A national survey interviewed 3800 people ages 18 and older nationwide by telephone. One question asked was the amount of gasoline they used in the previous week. Of those sampled, the average response was 11.75 gallons. A statistic in this situation is Select one: a. the 3800 people interviewed. b. 11.75 gallons. c. the fact that those interviewed are age 18 and older. d. All of the above

A pharmacist notices that a majority of his customers purchase a certain name brand medication rather than the generic—even though the generic has the exact same chemical formula. To determine if there is evidence that the name brand is more effective than the generic, he talks with several of his pharmaceutical colleagues, who agree to take each drug for two weeks, in a random order, in such a way that neither the subject nor the pharmacist knows what drug they are taking. At the end of each two-week period, the pharmacist measures their gastric acid levels as a response. The proper analysis is to use Select one: a. a one-sample t test. b. a matched pairs t test. c. a two-sample t test d. Any of the above. They are all valid so it is at the experimenter's discretion.

A random sample is collected of size n from a population with standard deviation and with the data collected a 95% confidence interval is computed for the mean of the population. Which of the following would produce a new confidence interval with smaller width (smaller margin of error) based on these same data? Select one: a. Increase σ. b. Use a smaller confidence level. c. Use a smaller sample size.

A shipment of small lab mice arrives at an animal care facility with a nominal weight of 10 g per mouse. A sample of 10 mice is selected and weighed. The technician wishes to test the hypothesis that the average weight of the mice matches the nominal value vs. that the mice are underweight at .05 level of significance. Here is some computer output on the analysis of this data:Which of the following is correct? Select one: a. The p-value is 0.07 and there is no evidence at the .05 level of significance that the mean weight is less than the nominal weight. b. The p-value is 0.04 and there is evidence at the .05 level of significance that the mean weight is less than the nominal weight. This is correct. Text reference: Section 17.4 The One-Sample t Test c. The p-value is 0.96 and there is no evidence at the .05 level of significance that the mean weight is less than the nominal weight. d. The p-value is 0.05 and there is no evidence at the .05 level of significance that the mean weight is less than the nominal weight.

Here is a histogram of T-cell velocities in vitro (in micrometers per minute): Which of the following statements is not true? Select one: a. The population distribution of T-cell velocities is most likely skewed to the right. b. A histogram of T-cell velocities would be more Normal if the researchers had collected more data. c. The sampling distribution of mean T-cell velocities for samples of size n = 100 is approximately Normal. d. The sampling distribution of mean T-cell velocities for samples of size n = 10 is very likely right-skewed.

It has been claimed that women live longer than men; however, men tend to be older than their wives. Ages of sixteen husbands and wives from England were obtained. These data should be analyzed with a Select one: a. two-sample t test. b. paired samples t test. This is correct. Husbands and their wives come naturally in pairs. We have two observations on each couple.Text reference: section 7.1. c. two-sample z test.

The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9.8 kg and standard deviation 0.1 kg. Reference: Ref 13-8 If you take a random sample of 16 adult men with liver cirrhosis, the sampling distribution of the average total body protein Select one: a. is approximately Normal, even though the population is skewed, because of the central limit theorem. b. is approximately Normal, because the population distribution is approximately Normal. c. might not be Normal at all, because the sample size is small. d. is definitely not Normal, because the sample size is small.

Which of the following statements about a density curve is (are) FALSE? Select one or more: a. A density curve always has area beneath it equal to 1. b. A density curve can adequately describe outliers observed in data. c. A density curve is always on or above the horizontal axis. d. A density curve comes in many shapes, some of which are symmetric while others are skewed. e. The area under a density curve above any range of values is the proportion of all observations that fall in that range.

You and your research partner carry out independent tests to study the effects of two new fertilizers that you have jointly developed—GrowMore and Enheightened. You each use a simple random sample from the population of size 50 and a significance level of 0.05. You find that the P-value for your hypothesis test regarding GrowMore is P = 0.053 and your partner finds that her P-value for Enheightened is P = 0.048. The proper conclusion from these outcomes is that Select one: a. GrowMore is a significantly worse fertilizer than Enheightened since the P-value was larger. b. even though the hypothesis tests lead to different conclusions, the P-values are so close together that there may not be any practical difference in their effectiveness. c. since both P-values are close to the significance level, neither fertilizer should be used. d. Enheigtened is the better fertilizer, and there is no reason to use GrowMore since it was not effective.

You are thinking of using a t procedure to construct a 95% confidence interval for the mean of a population. You suspect the distribution of the population is not Normal and may be skewed. Which of the following statements is correct? Select one: a. You should not use the t procedure since the population does not have a Normal distribution. b. You may use the t procedure provided your sample size is large, say at least 30. c. You may use the t procedure since it is robust to nonnormality.

Which of the following statements about the two-sample t procedures for significance tests and confidence intervals for the difference of the means, , is (are) True? Select one or more: a. The two population variances must be equal. b. The two samples must be simple random samples. c. Although Normality is a requirement, with large sample sizes the central limit theorem guarantees that the results will be approximately correct for other population distributions. d. The two samples must be independent.

B C and D

The nicotine content in cigarettes of a certain brand is Normally distributed with standard deviation 0.1 milligrams. The brand advertises that the mean nicotine content of their cigarettes is 1.5, but measurements on a random sample of 100 cigarettes of this brand gave a mean of 1.53. Is this evidence that the mean nicotine content is actually higher than advertised? Determine which of the following statements is (are) TRUE. Select one or more: a. The probability that H0 is true is 0.05. b. The data were statistically significant at α = 0.05. c. At the 5% significance level, Ha should be rejected. d. Even if nicotine content in cigarettes of this brand were not quite Normally distributed, the test would still be valid.

B and D

A college student is doing some research on the cost of one-bedroom apartments in town. He has randomly selected 25 apartments for which the price was published. The average price for these apartments is $652. He will assume that price follows a Normal distribution. Based on prices from previous years, a real estate agent gives him the information that σ is $55. A 95% confidence interval for μ is found to be 652 ± 21.56 = ($630.44, $673.56). Determine which of the following statements is true. Select one: a. A test of the hypotheses H0: μ = 650 vs. Ha: μ ≠ 650 would be rejected at the 0.05 level. b. A test of the hypotheses H0: μ = 650 vs. Ha: μ > 650 would be rejected at the 0.05 level. c. A test of the hypotheses H0: μ = 675 vs. Ha: μ ≠ 675 would be rejected at the 0.05 level. d. All of the above.

A random experiment was conducted to see if a newly formulated drug produced a different effect on the mean time to recovery than that achieved using the standard drug. It is known that the mean time to recovery for the standard drug is 26 days. Following an extensive random experiment involving 65 patients, the data gathered were used to construct a 95% confidence interval estimate for the mean recovery time (in days) for patients on the new drug. The 95% confidence interval was found to be (24.6, 27.8). What conclusion can be reached in this case concerning the new drug relative to the standard drug? Select one: a. There is evidence at the 0.05 level of significance that the new drug is better than the standard drug. b. The experimenter should reject the claim that the new drug is the same as the standard drug with respect to mean recovery time. c. There is insufficient evidence to reject the claim that there is no difference between the new drug and the standard drug with respect to mean recovery time. d. The confidence interval contains the hypothesized value for μ and hence it is significant at the 0.05 level. e. There is reason to believe that the standard drug is better than the new drug and hence the new drug should not be prescribed.

A stemplot of a set of data is roughly symmetric, but a quantile plot does not show a straight line. What conclusion can we draw? Select one: a. The data are Normal but not standard Normal. b. The data are standard Normal. c. The data are not Normal. d. The data are Normal.

A stemplot of a set of data is roughly symmetric, but the data do not even approximately follow the 68-95-99.7 rule. We conclude that the data are Select one: a. Normal, but they are not standard Normal. b. standard Normal. c. not Normal. d. Normal.

A test of significance is to be carried out on the H0: μ = 36 against the Ha: μ < 36 based on data from an SRS selected from a Normally distributed population variable. It was decided to use a level of significance of α = 0.02 to decide whether or not to reject the null hypothesis. The sample data produced a standard deviation of s = 15.6 based on 12 sample values. What values of would lead to the rejection of H0? Select one: a. > 46.5 b. < 26.7 c. < 25.5 d. > 45.3 e. Unable to determine with the information provided.

An instructor is teaching two sections of the same basic statistics course. The instructor is giving the same exams, homework assignments, and quizzes in both sections. Which t procedure should be used to determine if there is a difference in the academic performance between the two course sections? Select one: a. One-sample t test. b. Matched-pairs t procedure. c. Two-sample t test. d. None of the above.

Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz. Net weights actually vary slightly from bag to bag. Assume net weights are Normally distributed with standard deviation .4. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised. To do this, he selects 16 bags of tortilla chips of this brand at random and determines the net weight of each. He finds a mean of 13.88 oz with a standard deviation of 0.24 oz. What is the value of the test statistic? Select one: a. 0.50 b. 2.00 c. 1.2 d. 8.33 e. Cannot be determined f. None of the above.

Bags of a certain brand of tortilla chips claim to have a net weight of 14 oz. Net weights actually vary slightly from bag to bag. Assume net weights are Normally distributed. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised. To do this, he selects 16 bags of tortilla chips of this brand at random and determines the net weight of each. He finds a sample mean of 13.88 oz with a standard deviation of 0.24 oz. Suppose we were not sure if the distribution of net weights were Normal. In which of the following circumstances would we not be safe using a t procedure in this problem? Select one: a. The mean and median of the data are nearly equal. b. A histogram of the data is moderately skewed. c. A boxplot of the data shows the presence of a large outlier. d. The sample standard deviation is large.

I have computed a 95% confidence interval for the mean, μ, of a population as (13, 20). Based on this interval, we can say Select one: a. a null hypothesis that μ = 14 is not rejected at = 5%. b. a null hypothesis that μ = 24 is rejected at = 5%. c. Both choices are correct.

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled through weed and soil treatment. An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing ten seedlings, five were randomly selected throughout the field and assigned to receive Herbicide A. The remainder received Herbicide B. Soil and weeds for each seedling were treated with the appropriate herbicide, and at the end of the study period the height in (cm) was recorded for each seedling. The following results were obtained: Herbicide A8780807673Herbicide B7877746862 A 90% confidence interval for the difference in mean heights for the two herbicides is (0.2, 14.6). Which statement is correct? Select one: a. The P-value for a test of the null hypothesis of equal means and the alternative of different means would be greater than 10% since the interval doesn't include 0. b. A 95% confidence could not include zero either, since we would be even more confident of a difference in the groups. c. Both choices are incorrect.

Suppose a simple random sample of 100 observations is to be selected from the population and the sample average, , calculated. Which of the following statements about the distribution of is (are) FALSE? Select one or more: a. The distribution of will have a mean of 4. b. The distribution will be approximately Normal. c. Because the distribution shown in the histogram above is clearly skewed to the right, the shape of the distribution of will also show skewness to the right. d. Even though the distribution of the population variable appears to be skewed to the right, the distribution of will be approximately symmetric around μ = 4. e. The standard deviation of the distribution of will be 0.283.

Suppose that in the population of adult males, weights are normally distributed with standard deviation 24 pounds. A doctor records the weight of four adult male patients who come to his office one day and finds their mean weight to be 192.1 pounds. He computes a 90% confidence interval for the mean weight of all adult males based on his sample, and finds that it is 192.1 19.7 pounds. We may correctly conclude that Select one: a. he has made an error. The correct value is 192.1 23.5 pounds. b. if he continues to weigh groups of four of his male patients and compute a 90% confidence interval for each group, approximately 90% of these intervals will contain the true mean weight for the population of all adults males. c. Neither choice is correct because the sample is not an SRS.

After a week-long fishing trip in Brevard, NC, you and your friends have caught 100 rainbow trout. (You put some of them back!) The distribution of lengths of rainbows is known to have a standard deviation of 4 inches. From your sample you find an average of 22 inches. A 95% confidence interval for the true mean length of rainbow trout is Select one: a. 22 ± 0.08. b. 22 ± 0.78. c. 22 ± 0.93. d. not trustworthy. e. cannot be determined

Suppose the average Math SAT score for all students taking the exam this year is 480 with standard deviation 100. Assume the distribution of scores is normal. The senator of a particular state notices that the mean score for students in his state who took the Math SAT is 500. His state recently adopted a new mathematics curriculum and he wonders if the improved scores are evidence that the new curriculum has been successful. Since over 10,000 students in his state took the Math SAT, he can show that the P-value for testing whether the mean score in his state is more than the national average of 480 is less than 0.0001. We may correctly conclude that Select one: a. there is strong statistical evidence that the new curriculum has improved Math SAT scores in his state. b. although the results are statistically significant, they are not practically significant, since an increase of 20 points is fairly small. c. these results are not sufficient evidence that the new curriculum has improved Math SAT scores.

The air in poultry-processing plants often contains fungus spores, especially in the summer. Inadequate ventilation can affect the health of the workers. To measure the presence of spores, air samples are pumped to an agar plate and "colony forming units (CFUs)" are counted after an incubation period. An inspector for the Occupational Safety and Health Administration collects air samples from both the kill room and the processing room of a large poultry-processing plant on a random sample of 4 days over one summer. The data collected are matched pairs data, because Select one: a. the sample is too small for other procedures. b. the population standard deviation σ is not known. c. each day one measurement was taken from both rooms. d. there are exactly two groups: kill room and processing room.

The central limit theorem says that, when a simple random sample of size n is drawn from any population with mean μ and standard deviation σ, then when n is sufficiently large Select one: a. the standard deviation of the sample mean is σ 2 / n. b. the distribution of the population is exactly Normal. c. the distribution of the sample mean is approximately Normal. d. the distribution of the sample mean is exactly Normal.

The decrease in cholesterol level after eating a certain brand of oatmeal for breakfast for one month in people with cholesterol levels over 200 is Normally distributed with mean (in milligrams) μ and standard deviation σ = 3. The brand advertises that eating its oatmeal for breakfast daily for one month will produce a mean decrease in cholesterol of more than 10 points for people with cholesterol levels over 200, but you believe that the mean decrease in cholesterol is actually less than advertised. To explore this, you test the following hypotheses at the 0.05 level. H0 : μ=10, Ha : μ < 10 Reference: Ref 15-3 You obtain a P-value of 0.052. Which of the following is true? Select one: a. At the α = 0.05 significance level, you have proved that H0 is true. b. You have failed to obtain any evidence for Ha. c. There is some evidence against H0, and a study using a larger sample size may be worthwhile. d. This should be viewed as a pilot study, and the data suggest that further investigation of the hypotheses will not be fruitful at the α = 0.05 significance level.

The law of large numbers states that as the number of observations drawn at random from a population—with finite mean μ and variance σ—increases, the mean, , of the observed values Select one: a. tends to get larger. b. tends to get smaller. c. tends to get closer to the population mean μ. d. All of the above

The pH measurements of water specimens from various locations along a given river basin are Normally distributed with standard deviation 0.3. The average pH of water specimens from 4 randomly selected locations on this river basin is 7.8. If instead of 4 water specimens we had measured the pH of 16 water specimen, the a margin of error of a 95% confidence interval for μ would be Select one: a. four times as large. b. twice as large. c. half as large. d. one-fourth as large.

The sampling distribution of a statistic is Select one: a. the probability that we observed the statistic in repeated samples. b. the mechanism that determines if the randomization was effective. c. the distribution of values of the statistic over repeated samples from the population. d. the extent from which the sample results differ systematically from the truth.

The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. Reference: Ref 5-1 What is the sampling distribution of the sample mean score for a random sample of 36 students? Select one: a. Approximately Normal, but the approximation is poor. b. Approximately Normal, and the approximation is good. c. Exactly Normal. d. Neither Normal nor non-Normal. It depends on the particular 36 students selected.

Which of the following is not an assumption included in the simple conditions for inference about a mean? Select one: a. Simple random sampling with no nonresponse or other practical difficulty. b. Response variable has a perfect Normal distribution in the population. c. The population mean is known. d. The population standard deviation is known.

The power of a statistical test of hypotheses is Select one: a. the smallest significance level at which the data will allow you to reject the null hypothesis. b. equal to 1 - (P-value). c. the extent to which the test will reject both one- and two-sided hypotheses. d. defined for a particular alternative value of the parameter of interest and is the probability that a fixed level α significance test will reject the null hypothesis when the particular alternative value of the parameter is true.

A 95% confidence interval for the difference between population means, based on two independent samples of sizes 18 and 20, respectively, gives us (45.6, 56.7). Is the difference between the two population means, μ1 - μ2, included in the 95% confidence interval? Answer 1Choose...YesNoCan't tell Is the difference between the two sample means, - , included in the 95% confidence interval? Answer 2Choose...YesNoCan't tell Do 95% of the data values fall in the interval? Answer 3Choose...YesNoCan't tell

Can't tell Yes NO

A food company is developing a low-calorie granola bar, and the company is interested in whether the appeal of the packaging design for the new product is related to a person's gender. There were 100 male and 100 female volunteers available for purposes of evaluation. Both males and females rated the design on a scale of 1 to 10, with 1 being "very unappealing" and 10 being "very appealing." The mean rating for males was = 7.4, with a standard deviation = 1.5. The mean rating for females was = 8.0, with a standard deviation = 2.0. Let μ1 and μ2represent the mean ratings we would observe for the populations of males and females, respectively, and assume our samples can be regarded as samples from these populations. Reference: Ref 18-7 Which of the following would lead us to believe that the t procedures were not safe to use here? Select one: a. The sample medians and means for the two groups were slightly different. b. The distributions of the data were moderately skewed. c. The data are integers between 1 and 10 and so cannot be normal. d. The market analysts deemed that the volunteers could not be considered a simple random sample from the population.

A national survey interviewed 3800 people ages 18 and older nationwide by telephone. One question asked was the amount of gasoline they used in the previous week. Of those sampled, the average response was 11.75 gallons. If the survey had interviewed only 1000 people, which of the following would be true? Select one: a. By the law of large numbers, the average amount of gasoline used would again be 11.75 gallons. b. By the law of large numbers, the average amount of gasoline in the sample of 1000 people would have to be farther from the true mean amount of gasoline used by all people age 18 and older than the average found in the sample of 3800 people. c. The average income computed from the sample of 1000 people would be more accurate because smaller samples tend to be more homogeneous than larger samples. d. None of the above

A radio show runs a phone-in survey each morning. One morning the show asked its listeners whether the city should change regulations for new structures at local beachfront property in order to save certain sea grass populations. The majority of those phoning in their responses answered, "No, it is just grass—there is no reason to worry about it," and the station reported the results as statistically significant. We may safely conclude Select one: a. that there is strong evidence that the city council should change regulations. b. that it is unlikely that, if all Americans were asked their opinion, the result would differ from that obtained in the poll. c. that there is strong evidence that the city council should not change regulations. d. very little other than that the majority of those phoning in their responses believe there is no reason to care about sea grass.

A researcher wishes to determine if aerobic exercise improves mental performance immediately following the exercise. He plans to have high school students participate in 30 minutes of aerobic exercise and then take a standard test of their reasoning skills. Suppose the scores of high school students on this test of reasoning skills immediately after 30 minutes of aerobic exercise follow a Normal distribution with mean μ and standard deviation σ = 4. Suppose also that, in the general population of all high school students, scores on the test of reasoning skills follow a Normal distribution with mean 25 and standard deviation σ = 4. The researcher, therefore, decides to test the following hypotheses. H0 : μ = 25, Ha : μ > 25 To do so, the researcher has 10,000 high school students do 30 minutes of aerobic exercise and then, immediately following the exercise, take the test. The mean score for these students is = 25.2 and the P-value is less than 0.0001. Reference: Ref 15-1 It is appropriate to conclude which of the following? Select one: a. The researcher has conclusively proved that, for high school students, 30 minutes of aerobic exercise substantially improves mental performance. b. The researcher has strong evidence that, for high school students, 30 minutes of aerobic exercise substantially improves mental performance. c. The researcher has moderate evidence that, for high school students, 30 minutes of aerobic exercise substantially improves mental performance. d. None of the above

Correct 1.00 points out of 1.00 Flag question Question text Does taking Vitamin D increase the mean lifespan of a rat? A sample of 20 rats was randomized to group 1 (control) and group 2 (Vitamin D). The lifespan (days) of each rat was measured. Here is some of the output:Which of the following is correct? Select one: a. Because 10 rats were randomized to each of the two groups, a matched pairs design could be used. b. About 95% of rats in group 1 have lifetimes between 470 days and 590 days. c. Because the two standard deviations are about equal, there is no evidence that the average lifetimes are different. d. The standard errors measure how much the average lifetime for each group could vary if new samples of 10 rates were taken.

Does 30 minutes of meditation every day provide significant improvement in mental performance? To investigate this issue, a researcher conducted a study with 150 adult subjects who meditated for 30 minutes each day for a period of six months. At the end of the study, 300 variables related to the mental performance of the subjects were measured on each subject and the means compared to known means for these variables in the population of all adults. Sixteen of these variables were significantly better (in the sense of statistical significance) at the α = 0.05 level for the group that performed 30 minutes of meditation each day as compared to the population as a whole, and three variables were significantly better at the α = 0.01 level for the group that performed 30 minutes of meditation each day as compared to the population as a whole. It would be correct to conclude that Select one: a. there is very good statistical evidence that 30 minutes of meditation each day provides some improvement in mental performance. b. there is very good statistical evidence that 30 minutes of meditation each day provides some improvement for the variable that was significant at the α = 0.01 level. We should be somewhat cautious about making claims for the variables that were significant at the α = 0.05 level. c. these results would have provided very good statistical evidence that 30 minutes of meditation each day provides some improvement in mental performance if the number of subjects had been larger. It is premature to draw statistical conclusions from studies in which the number of subjects is lower than the number of variables measured. d. None of the above

In a recent online poll regarding public opinion on wildlife preserves, it was indicated that a majority (92%) of Americans favored additional preserves. The margin of error for the poll was reported to be ±0.5% based on 4700 respondents. It can be concluded that Select one: a. the margin of error is small, so the poll must be accurate. b. there were a lot of respondents, so the poll must be trustworthy. c. certainly a majority of Americans are in favor of additional preserves since the percent in favor is so large and the margin of error is so small. d. since the margin of error only accounts for sampling error, other errors (such as undercoverage) have probably made the results useless.

In a test of statistical hypotheses, what does the P-value tell us? Select one: a. If the null hypothesis is true. b. If the alternative hypothesis is true. c. The largest level of significance at which the null hypothesis can be rejected. d. The smallest level of significance at which the null hypothesis can be rejected.

In a test of statistical significance, the p-value tells us Select one: a. if the null hypothesis is true. b. if the alternative hypothesis is true. c. the largest level of significance at which the null hypothesis can be rejected. d. the smallest level of significance at which the null hypothesis can be rejected.

In assessing the validity of any test of hypotheses, it is good practice to Select one: a. examine the probability model that serves as a basis for the test by using exploratory data analysis on the data. b. determine exactly how the study was conducted. c. determine what assumptions the researchers made. d. All of the above

In tests of significance about an unknown parameter, what does the test statistic represent? Select one: a. The value of the unknown parameter under the null hypothesis. b. The value of the unknown parameter under the alternative hypothesis. c. A measure of compatibility between the null and alternative hypotheses. d. A measure of compatibility between the null hypothesis and the data.

People tend to give more socially acceptable answers when asked a sensitive question in person rather than anonymously via computer. When computing a 95% confidence interval for a population parameter, the margin of error Select one: a. covers all deviations from the parameter that are due to answer bias. b. covers 95% of deviations from the parameter that are due to answer bias. c. covers deviations from the parameter that are due to answer bias as long as the sample was a random sample. d. does not cover the deviations from the parameter that are due to answer bias.

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution with mean 115 and standard deviation σ = 25. You suspect that incoming freshman have a mean μ, which is different from 115, since they are often excited yet anxious about entering college. To verify your suspicion, you test the following hypotheses. H0 : μ = 115, Ha : μ 115 You give the SSHA to 25 incoming freshmen and find their mean score. Based on this, you reject H0 at significance level α = 0.01. Which of the following would be most helpful in assessing the practical significance of your results? Select one: a. Test the hypotheses again, this time using significance level α = 0.001. b. Report the P-value of your test. c. Take another sample and retest just to make sure the results are not due to chance. d. Construct a 99% confidence interval for μ to see the magnitude of the difference between 115 and your sample results.

The level of nitrogen oxides (NOX) in the exhaust of cars of a particular model varies Normally with standard deviation σ = 0.05 grams per mile (g/mi). Government regulations call for NOX emissions no higher than 0.3 g/mi. In testing H0 : μ = 0.3 versus Ha : μ < 0.3 using significance level 0.05, we find that the power of this test against an alternative of μ = 0.28 based on a random sample of size n = 40 is 0.808. Reference: Ref 15-5 Using a more lenient significance level of 0.10 would Select one: a. decrease the power of this particular test and decrease the probability of a Type I error. b. increase the power of this particular test and decrease the probability of a Type I error. c. decrease the power of this particular test and increase the probability of a Type I error. d. increase the power of this particular test and increase the probability of a Type I error.

Which of the following is correct? Select one: a. Two-sample procedures should be used with matched pairs designs. b. If some of the matched pairs are missing some data, use a two-sample procedure as it does not require equal sample size in each group. c. The sample sizes in each group need to be equal to use two-sample procedures. d. Two-sample procedures can be used with random samples from each group and for experiments where a single population is randomized to the two groups.

Which of the following statements about the mean and the median of a density curve are FALSE? Select one: a. The median is the point on the axis that divides the area under the density curve in two equal halves. b. The median and the mean have the same value if the density curve is symmetric. c. The mean is the "balance point" of the density curve. d. The median of a skewed density curve is pulled away from the mean in the direction of the long tail. e. For a symmetric density curve, both the mean and the median are at the center of the curve.

Which of the following would lead us to believe that the t procedures were not safe to use in a two-sample problem with 100 subjects in each group? Select one: a. The same medians and means for the two groups were slightly different. b. The distribution of the data values were moderately skewed. c. The data was only integers so cannot be Normally distributed. d. Several outliers were detected in each group.

You carry out a study to investigate the decline in cod populations off the coast of Canada. In order to carry out a hypothesis test, you must decide what sample size should be used. What factors affect your decision? Select one: a. α b. β c. Effect size d. All of the above

A first aid cream contains amounts of the active ingredient (in mg) that vary from tube to tube. You select a simple random sample of 9 tubes and assess the quantity of active ingredient they contain. The 9 amounts, in mg, are 23 24 23 29 28 26 27 28 26 Based on these data, a 99% confidence interval for the population mean μ has margin of error Select one: a. 2.50 mg. b. 1.92 mg c. 2.42 mg d. 0.75 mg e. Cannot be determined.

If the level of confidence were changed from 98% to 95%, what would happen to the confidence interval and the P-value? Select one: a. The confidence interval would become longer and the P-value would decrease. b. The confidence interval would become shorter and the P-value would increase. c. The confidence interval would not change and the P-value also would not change. d. The confidence interval would become shorter and the P-value would decrease. e. The confidence interval would become shorter but the P-value would not change.

We are interested in testing a null hypothesis about a population mean μ being equal to a specified value using a simple random sample of size 25. In the past the population variable has shown a slight tendency to non-Normality (slight skewness but no strong outliers). Why can we safely use a t procedure in this testing situation? Select one: a. The sample standard deviation is robust against such things as outliers. b. The one-sample t procedure requires that the sample be selected using an SRS design, which is what was done in this case. c. The t procedures are quite robust against non-Normality, unless there are strong outliers. d. All of the above. e. Only B and C are justifications for using the t procedure here.

Which of the following statements about the standardized z-score of a value of a variable X, which has a mean of m and a standard deviation of s, is (are) TRUE? Select one: a. The z -score has a mean equal to 0. b. The z-score has a standard deviation equal to 1. c. The z-score tells us how many standard deviation units the original observation fall away from the mean. d. The z-score tells us the direction the observation falls away from the mean. e. All of the above statements about the z-score are true.

When planning a two sample design, it is best to use a different sample size for each sample. Select one: True False

False

The two-sample z statistic is used when the population mean is known from both samples. Select one: True False

False (should be population stnd. deviation)

The margin of error in a confidence interval captures errors that are present from random sampling only. Select one: True False

True

Determine whether each of the following statements regarding a Normal density curve is true or false. It is symmetric. It has a peak centered above its mean. The quartiles lie 1 standard deviation below and above the mean. The spread of the curve is proportional to the standard deviation.

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