Economic and Business Statistics week 11+
Suppose you want to estimate the proportion of students at a large university that approve of the new health care bill. From an SRS of 1000 university students, 778 approve of the health care bill. What is the margin of error for a 99% confidence interval for p?
0.034
Suppose you want to estimate the proportion of students at a large university that approve of the new health care bill. From an SRS of 1000 university students, 778 approve of the health care bill. What is the margin of error for a 99% confidence interval for p? Give your answer to three decimal places
0.034
Multiple-comparisons methods are commonly used only under what circumstance?
After rejecting H0
Jessica believes that her 2-hour typing class is so good that she can improve senior citizen's speed significantly in the short amount of time. 15 senior citizens come to her class and she tests their wpm before and after her course. Using the sign test & the Normal approximation to Binomial, Jessica's p-value value for this analysis is ______ (4 decimal places) and the null hypothesis is _______. Please choose the correct answer from the following choices, and then select the submit answer button. 0.0302, rejected
0.2119, not rejected
Small samples create a particular difficulty for statistical analysis because ________. Content_hint: This is a basic concept of the section
All of the above
Because the analysis of variance F test is robust and provided the sample sizes are large enough, we can still make valid conclusions from the test results when which of the following conditions is not met?
All populations have a Normal distribution.
A potential candidate for President has stated that she will run for office if at least 30% of Americans voice support for her candidacy. To make her decision she draws a random sample of 500 Americans. Suppose that in fact 35% of all Americans support her candidacy. The mean of the sampling distribution of p^ is _______.
0.35
Fill in the Blank: Sara used a sample size of 12 for each of two comparison groups. If she had no pre-determined values of p1 and p2 and used a 95% confidence interval, what was her margin of error? Round to the nearest tenth.
0.4
A survey was conducted on religious practices in the United States. Among other questions, respondents were asked their gender and whether they prayed at least once a day. The following table summarizes these data: What proportion of males said they pray at least once a day? Please give your answer to 2 decimal places. (X.XX)
0.49
Using the sample size formula, you will get the largest sample size when you choose a p* of ________. Use one decimal place in your answer.
0.5
A survey was conducted on religious practices in the United States. Among other questions, respondents were asked their gender and whether they prayed at least once a day. The following table summarizes these data: On the basis of these data, what is the pooled sample proportion for the proportion of respondents in the survey who said that they pray at least once a day? Give your answer to 3 decimal places. (X.XXX)
0.582
In a survey of college students at a large university, students were asked their gender and whether they liked country music. The following table summarizes these data: What proportion of the female students like country music? Please give your answer to 3 decimal places. (X.XXX)
0.682
Which of the following is a statistical method for comparing several population means for equality?
Analysis of Variance
Can scented coupons increase sales? Three different coupons for juice were mailed to households - U (unscented), A (apple scented), and C (citrus scented). The number of cartons of the juice purchased with each type of coupon was measured at a store. The ANOVA p-value was < 0.001. Here are the results of a multiple comparison method following an ANOVA: The estimate of the contrast that compares the mean of the unscented group to the average of the other two groups is about:
0.73
A study was conducted on caffeine consumption by children. The parents of 104 children aged 5-7 and 97 children aged 8-12 were surveyed about whether their child consumed caffeine. The following table summarizes these data: On the basis of these data, what is the pooled sample proportion for the proportion of children in the sample who consume caffeine? Give your answer to 3 decimal places. (X.XXX)
0.7662
Suppose p^ is 0.80 and the margin of error is 0.03. Calculate the 99% confidence interval for p. Enter your answer using two decimal places and separating the ends of the interval with a comma.
0.77, 0.83
Can scented coupons increase sales? Three different coupons for juice were mailed to households - U (unscented), A (apple scented), and C (citrus scented). The number of cartons of the juice purchased with each type of coupon was measured at a store. The following is the output from an analysis of the experiment: The estimate of the within-group standard deviation is about:
0.78
Jessica believes that her 2-hour typing class is so good that she can improve senior citizen's speed significantly in the short amount of time. 15 senior citizens come to her class and she tests their wpm before and after her course. Using the sign test & the Normal approximation to Binomial, a Z value for this analysis is ______ (4 decimal places).
0.8018
How does seat belt use vary with drivers' race or ethnic group? The answer depends on gender (males are less likely to buckle up) and also on location. Here are data on a random sample of male drivers observed in Houston: The total number of drivers observed was ______
1,166
An environmental group conducts a study to measure energy consumption in a large metropolitan city as measured by the amount of gasoline purchased. In a random sample of 14 vehicle owners on a particular day, they calculated a mean of 13.62 gallons and a standard deviation of 3.92 gallons. Thus, the standard error of the sample mean is ________ gallons. (Give your answer rounded to 2 decimal places.)
1.05
The supervisor of a fish hatchery measures the length of a particular species every week after hatching to track their growth. If their average length is too short or too long, they are not maturing properly and further tests must be done to determine the cause. She randomly selects 30 fish from among those that hatched five weeks ago and observes a mean length of 10.1 inches and a standard deviation of 1.7 inches. What is the value of the test statistic if the population mean length for these fish should be 9.7 inches? . Note that because the sample mean is more than 9.7, the test statistic is positive.]]
1.289 [[This can be found using the formula for the one-sample t statistic, t = ( - μ)/(s / √n)
You are starting to investigate the difference between successful and unsuccessful tech startup companies, where the population variance is equal. You look at the average revenue of 'failed' companies and 'successful' companies as of 'Series B' funding time. You find that the 53 failed companies have an average revenue of 42 million dollars per year with a sample standard deviation of 3 million dollars per year. You find that the 21 successful companies have a mean revenue of 64 million dollars per year with a sample standard deviation of 9 million. The standard difference in mean revenue between successful and failed startups is _____ (two decimal places).
1.44
To calculate the confidence interval using the "Plus 4" or the Wilson method still requires a sample size of at least
10
To calculate the confidence interval using the "Plus 4" or the Wilson method still requires a sample size of at least ______.
10
About 13% of people in the United States are left handed. One university planned a large 150-seat auditorium lecture hall with 15% "left handed" seats. A class that filled the auditorium ran out of these seats because there were 18% left-handers in the class. The mean of the sampling distribution for the proportion of left-handers in the class should be _____. Enter your answer as a percent.
13
About 13% of people in the United States are left-handed. One university planned a large 250-seat auditorium lecture hall with 15% "left-handed" seats. A class that filled the auditorium ran out of these seats because there were 18% left-handers in the class. The mean of the sampling distribution for the proportion of left-handers in the class should be __________.
13%
Below is a table showing the results of a simple random sample asking respondents what types of cars they drive and their commuting distance to work in miles. This table has _____ columns.
2
In the model of examining independence in two-way tables, a simple random sample of size n is selected from a population and _________ categorical variables are measured for each individual.
2
The director of a customer service center wants to estimate the mean number of customer calls the center handles each day, so he randomly samples records from 48 different days. To create a 95% confidence interval for the true mean number of calls, the correct value of t* to be used is ________.
2.021
Suppose you will calculate a 95% confidence interval for μ based on a simple random sample of 25 individuals. The critical value for this confidence interval is t* =
2.064
The critical value for a 95% confidence interval when there are n = 13 observations is
2.179
Below is a table showing the results of a simple random sample asking respondents what types of cars they drive and their commuting distance to work in miles. Minitab gives the following table of observed and expected counts. The contribution to the chi-square statistic from full-size cars driven at least 20 miles for commuting is
2.558
Use Table D in the text to find the critical value for a 99% confidence interval when there are n = 24 observations ________. Give your final exam to three decimal places.
2.807
Suppose you will calculate a 99% confidence interval for μ based on a simple random sample of 21 individuals. What is the critical value t* to be used?
2.845
There is longstanding belief that taking birth control pills might cause women to gain weight. A study on how birth control pills might affect basal metabolism found that the average basal metabolism rate from n = 24 women who had used oral contraceptives at least six months was 5841 kilo Joules per day (kJ/d) and the average basal metabolism rate from n = 22 women who had never used birth control was 5633 kilo Joules per day (kJ/d) (Diffey, Piers, Soares, and O'Dea. "The effect of oral contraceptive agents on the basal metabolic rate of young women." British Journal of Nutrition. June 1997.) Inference using two-sample t procedures and the conservative degrees of freedom will have how many degrees of freedom?
21
Here is a two-way table of Census Bureau data describing the age and sex of all American undergraduate college students. The table entries are counts in thousands of students. Males age 20 to 24 are what percent of college students?
23.3%
Jake hypothesizes that, in California, homes sell for significantly higher in May than in August. He also believes both months to have the same variance if they are within the same calendar year. He looked at a sample of 250 homes which sold in May versus 300 homes which sold in August of the same year. He found the May sold homes to have a mean sale price of $614,000 with a sample standard deviation of $28,000. He found the mean sales price of homes in August to be $608,000 with a standard deviation of $22,000. The pooled estimator of σ is ______
24906
Do students tend to improve their GMAT scores the second time they take the test? A random sample of four students who took the test twice received the following scores: Student 1 2 3 4 First score 450 520 720 600 Second score 440 600 720 630 Assume that the changes in GMAT scores (second score - first score) have an approximate normal distribution. A 90% confidence interval for the mean change in score is:
25 ± 47.5
The director of a customer service center wants to estimate the mean number of customer calls the center handles each day, so he randomly samples records from 26 different days. The sample yields a mean of 258.4 calls with a standard deviation of 32.7 calls per day. The 95% confidence interval for the mean number of calls per day has an upper bound of ________.
271.6
An experiment was conducted to see if elderly patients had more trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups. The researchers conducted the experiment and obtained data summarized in the following table: The standard error of the difference in sample means is ________. Answer to three decimal places.
3.563
Sam is doing a study comparing adults and children in swim lessons. This study will use a 98% confidence interval that will have a margin of error of 0.3 or less. What sample size should Sam use for the adults and children?
30
What sample size would be used in a two-sample study using a 90% confidence interval with a margin of error of 0.2 or less when we assume p1 = 0.65 and p2 =0.58?
32
A shipment of 20,000 bags of oranges arrives at a distribution center with a nominal weight of 3200 g per bag. A sample of 10 bags is selected and weighed. The average weight of the sample is 3300g, and the standard deviation of weight among cartons is 80 g. Find a 95% confidence interval for the mean weight of all the bags of oranges in the shipment.
3300 ± 57.3
In a survey of college students at a large university, students were asked their gender and whether they liked country music. Here are the data: In analyzing these data, the researchers tested whether the proportions of males and females who like country music are significantly different. Considering females to be population 1 and males to be population 2, the hypotheses for this test are: H0: p 1 = p2 versus Ha: p1 ≠ p2 Using p^1 = 0.683, p^2 = 0.458, what is the value of the test statistic? Note: The denominator of the test statistic is: √0.002858=0.0535. Report your test statistic to three decimal places. (X.XXX)
4.206
A sample of n = 53 individuals participated in a comprehensive chess program to determine if it would have a positive effect on reading scores. After the program, each individual took a reading test. The average of the test scores was 63.07, and the standard deviation was 17.84. A 95% confidence interval for the true mean score for reading ability after taking the comprehensive chess program is 63.07 ± ________. (Give your answer rounded to 2 decimal places.)
4.92
A statistics teacher was interested in looking at the possible effects that working for pay had on her students. One question she was interested in was how many hours students work for pay, since that could have an impact on the time available for studying. She asked a sample of students to fill out a questionnaire about their study and work habits. Some of the results are shown below. Females represent ____ % of students represented here. Answer to tenths of a percent.
45.8
The sample size needed for testing the null hypothesis for a population proportion of 0.22 using a two-sided test with α = 0.05 and 80% power when the comparison proportion is 0.4 is _______________.
47
What sample size is required for a significance test that the two proportions are equal, using a two-sided alternative with p1 =0.42 and p2 =0.51, α = 0.05, and 80% power. Use technology
481
To calculate the confidence interval using the "Plus 4" or the Wilson methods, we add ____ trials and ____ "successes." Enter the two values separated by a semicolon.
4;2
One may use the two sample t-procedure in as small of a sample size as n1 = n2 =____ where data is Normal and there are no outliers.
5
Students in a simple random sample of fourth, fifth, and sixth graders were asked which of the three following choices is most important to them: making good grades, being popular, or participating in sports. Also recorded was the student's gender. The proportion of females who said grades were most important is
51.8
Use technology to find the sample size needed for testing the null hypothesis for a population proportion of 0.81 using a two-sided test with α = 0.02 and 80% power. Use 0.96 as the comparison proportion
52
What sample size would be used in a two-sided, two-sample study using α = 0.1 and 80% power when we assume p1 =0.65 and p2 =0.58? Use technology.
597
A randomized, double blind clinical study was conducted on adults aged 50 to 59 to test the effectiveness of a new vaccine for shingles (skin blisters caused by a virus). Approximately, half of the participants were randomly assigned to the vaccine group and the rest to the placebo group. Participants were monitored for at least a year after receiving either the vaccine or the placebo for occurrence of shingles. The following table summarizes these data: Those who developed the new vaccine want to show that the proportion of those who get shingles is less for those receiving the vaccine than those who don't. Letting those who receive the vaccine be treatment 1 and those receiving the placebo be treatment 2, the appropriate hypotheses for this test are: H0: p 1 = p2 versus Ha: p1 < p2 Using p^1 = 0.002676, p^2 = 0.008817, what is the value of the test statistic? Note: The denominator of the test statistic is: =0.001094. Use all decimal places as given in your computations and report your test statistic to three decimal places. (X.XXX)
6.084
A statistics teacher was interested in looking at the possible effects that working for pay had on her students. One question she was interested in was how many hours students work for pay, since that could have an impact on the time available for studying. She asked a sample of students to fill out a questionnaire about their study and work habits. Some of the results are shown below. What percent of these students work more than 20 hours per week?
6.8%
Below is a table showing the results of a simple random sample asking respondents what types of cars they drive and their commuting distance to work in miles. What percent of the people in the sample drive compact cars?
61/250 = 24.4%
Suppose there are three distinct routes that connect your home to school. Every morning, you roll a die to randomly choose which of the three routes you will use that day. You record the amount of time in minutes it takes to commute to school to test whether there is a significant difference in the mean amount of time each route takes. After three months, you summarize the data. Stemplots for the times from each of the three routes are roughly Normal. The distribution to be used for the ANOVA test with this study is F(2, ________).
65
Below is a table showing the results of a simple random sample asking respondents what types of cars they drive and their commuting distance to work in miles. What percent of the people in the sample drive less than 20 miles to work?
70
Use of the plus four method requires a confidence level of at least _____ percent.
90
Jake hypothesizes that, in California, homes sell for significantly higher in May than in August. He also believes both months to have the same variance if they are within the same calendar year. He looked at a sample of 250 homes which sold in May versus 300 homes which sold in August of the same year. He found the May sold homes to have a mean sale price of $614,000 with a sample standard deviation of $28,000. He found the mean sales price of homes in August to be $608,000 with a standard deviation of $22,000. The pooled estimator of σ is ______ (nearest whole number).
$24,906
Expected counts in a two-way table are
(row total) x (column total) / (table total)
This question requires a graphing calculator or software. Theoretically, regular exercise makes the heart pump more efficiently, so normally it would not have to beat as often. A researcher wants to examine this effect in a population of college-age students. The resting heart rates for 20 students who exercise regularly had mean 63.2 beats per minute and standard deviation 5.3 beats per minute. The resting heart rates for 25 students who do not exercise regularly had mean 73.4 beats per minute and standard deviation 8.9 beats per minute. What is a 98% confidence interval for the difference in average heart rate attributable to exercise? Use the exercisers as group 1 and round to the hundredths place. Enter the two ends separated by ;.
-15.35; -5.02
A tire manufacturer claims that one particular type of tire will last at least 50,000 miles. A group of angry customers do not believe this is so. They take a sample of 14 tires and want to test if the mean mileage of the tires is really 50,000. The customers found that the average tire life of the sampled tires was 49,294 miles and the standard deviation was 870 miles. What is the value of the test statistic?
-3.036
A randomized, double blind clinical study was conducted on adults aged 50 to 59 to test the effectiveness of a new vaccine for shingles (skin blisters caused by a virus). Approximately, half of the participants were randomly assigned to the vaccine group and the rest to the placebo group. Participants were monitored for at least a year after receiving either the vaccine or the placebo for occurrence of shingles. The following table summarizes these data: What proportion of those in the vaccine group got shingles? Please give your answer to 4 decimal places. (X.XXXX)
.0027
A randomized, double blind clinical study was conducted on adults aged 50 to 59 to test the effectiveness of a new vaccine for shingles (skin blisters caused by a virus). Approximately, half of the participants were randomly assigned to the vaccine group and the rest to the placebo group. Participants were monitored for at least a year after receiving either the vaccine or the placebo for occurrence of shingles. The following table summarizes these data: What proportion of those in the placebo group got shingles? Please give your answer to 4 decimal places. (X.XXXX)
.0088
Here is a two-way table of Census Bureau data describing the age and sex of all American undergraduate college students. The table entries are counts in thousands of students. The conditional probability of a female student being 25 to 34 years old is _____ (give your answer to three decimal places).
.114
A survey was conducted on religious practices in the United States. Among other questions, respondents were asked their gender and whether they prayed at least once a day. The following table summarizes these data: Give the difference in the proportion of females who said they pray at least once a day and the proportion of males who said they pray at least once a day. Please give your answer to 2 decimal places. (X.XX)
.17
Fill in the Blank: A survey was conducted within city limits asking respondents if they were happy. Results, categorized by men/women, are below. The p-value (using technology) is ________________ and therefore at 95% confidence, we cannot conclude there is a difference between happiness of men and women
.406
A study was conducted on caffeine consumption by children. The parents of 104 children aged 5-7 and 97 children aged 8-12 were surveyed about whether their child consumed caffeine. The following table summarizes these data: What proportion of 8-12 year olds consumes caffeine? Please give your answer to 2 decimal places (X.XX).
.80
You may use a two sample t-test in the following situation: n1 = 10 and n2 = 10, data is close to Normal, _____ outliers present and no skewness.
0
A tire manufacturer claims that one particular type of tire will last at least 50,000 miles. A group of angry customers do not believe this is so. They take a sample of 14 tires and want to test if the mean mileage of the tires is really 50,000. From the data, the customers calculate a test statistic of -3.254. What is the range for the corresponding P-value?
0.0025 < P-value < 0.0050
A randomized, double blind clinical study was conducted on adults aged 50 to 59 to test the effectiveness of a new vaccine for shingles (skin blisters caused by a virus). Approximately, half of the participants were randomly assigned to the vaccine group and the rest to the placebo group. Participants were monitored for at least a year after receiving either the vaccine or the placebo for occurrence of shingles. The following table summarizes these data: What proportion of those in the vaccine group got shingles? Please give your answer to 4 decimal places. (X.XXXX)
0.0027
Researchers performed a study on the effects of a nonsteroidal anti-inflammatory drug (NSAID) given before and after arthroscopic knee surgery. A sample of 67 patients undergoing elective knee arthroscopy was randomly divided into three treatment groups. Researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery. The probability that the researchers would have seen differences among the mean pain scores as extreme or more extreme than the observed sample results is ________.
0.012
Can scented coupons increase sales? Three different coupons for juice were mailed to households - U (unscented), A (apple scented), and C (citrus scented). The number of cartons of the juice purchased with each type of coupon was measured at a store. The following is the output from an analysis of the experiment: Which of the following is correct?
Based on the overlap of the confidence intervals, there is little evidence to separate the means of the two scented groups.
This question requires a graphing calculator or software. Theoretically, regular exercise makes the heart pump more efficiently, so normally it would not have to beat as often. A researcher wants to examine this effect in a population of college-age students. The resting heart rates for 20 students who exercise regularly had mean 63.2 beats per minute and standard deviation 5.3 beats per minute. The resting heart rates for 25 students who do not exercise regularly had mean 73.4 beats per minute and standard deviation 8.9 beats per minute. What is a 98% confidence interval for the difference in average heart rate attributable to exercise?
Based on these samples, we can say that regular exercise in college-age people decreases the resting heart rate by an average of 5.02 to 15.35 beats per minute, with 98% confidence.
A shipment of 20,000 bags of oranges arrives at a distribution center with a nominal weight of 3200 g per bag. A sample of 10 bags is selected and weighed. The auditor wishes to test the hypothesis that the average weight of the bags matches the nominal value vs. that the bags are overweight at α = 0.05. Here is some computer output on the analysis of this data. Based on the output above, which of the following is correct?
Because the 95% confidence interval excludes the value 3200, there is evidence that the mean weight differs from the nominal weight
An experiment on the effectiveness of gingko biloba in helping boost memory function randomly assigned half the subjects to gingko and the other half to a placebo. At the end of the study, a 95% confidence interval for the difference in mean scores (gingko - control) on a memory function test is (-2.34, 4.39). Based on this information, what can we conclude?
Because the interval contains 0, it is reasonable that there is no difference in average memory function between people who take gingko and those who do not
A study was conducted on caffeine consumption by children. The parents of 104 children aged 5-7 and 97 children aged 8-12 were surveyed about whether their child consumed caffeine. The following table summarizes these data: What parameter compares the proportion of children who consume caffeine in the two-age groups?
Difference between the proportion of all children aged 5 to 7 who consume caffeine and the proportion of all children aged 8 to 12 who consume caffeine.
A group of psychologists was interested in knowing if living environment had any effect on a student's grade point average (GPA). They took a set of twins and randomly assigned one twin to live in an urban area and the other twin to live in a rural area. After one year, they computed the GPAs for the twins and looked at the differences. Then they calculated the test statistic, and the P-value was found to be between 0.20 and 0.25. What can you conclude if the level of significance is 0.05?
Do not reject H0 and say there is insufficient evidence to suggest that a difference exists between the mean GPAs.
A sociologist is interested in determining if the mean GPA is the same for students in all four undergraduate class levels. Assume all populations are normally distributed and all population variances are equal. She wishes to test the following hypotheses to determine if there is evidence that the mean GPA differs. 𝐻𝑜:𝜇1=𝜇2=𝜇3=𝜇4 Ha: At least one class level has a different mean GPA. If the ANOVA F test yields P = 0.42. What should we conclude?
Do not reject Ho and conclude there is no evidence the mean GPA differs for the four undergraduate class levels.
True or False: In the Model for one-way ANOVA, the pooled standard error sp is a parameter.
FALSE
A study was conducted on caffeine consumption by children. The parents of 104 children aged 5-7 and 97 children aged 8-12 were surveyed about whether their child consumed caffeine. For the 8-12 year old children, 80% consumed caffeine and 73% of the 5-7 year old children consumed caffeine. A 95% confidence interval was computed as (0.80 - 0.73) ± (1.96)(0.05954) or (-0.05, 0.19) where SE = 0.05954. True or false: The 95% confidence interval (-0.05, 0.19) estimates the difference between the sample proportion of 8-12 year olds who consume caffeine and the sample proportion of 5-7 year olds who consume caffeine.
False
If the null hypothesis is ________, the observed variability in the sample means will be greater than the variability you would expect if the means are equal.
False
This question requires a graphing calculator or software. Theoretically, regular exercise makes the heart pump more efficiently, so normally it would not have to beat as often. A researcher wants to examine this effect in a population of college-age students. The resting heart rates for 20 students who exercise regularly had mean 63.2 beats per minute and standard deviation 5.3 beats per minute. The resting heart rates for 25 students who do not exercise regularly had mean 73.4 beats per minute and standard deviation 8.9 beats per minute. Based on these samples, we can say that individuals who exercise regularly will decrease the resting heart rate by 5.02 to 15.35 beats per minute, with 98% confidence.
False
True or False: A potential candidate for President has stated that she will run for office if at least 30% of Americans voice support for her candidacy. To make her decision she draws a random sample of 500 Americans. Suppose that in fact 35% of all Americans support her candidacy. The mean of the sampling distribution of p^ is 0.30.
False
True or False: A reasonable design for an experiment to evaluate a new teaching method might be to have all the students take a pretest, randomly assign half to the new method and half to the standard method, then have all students take a test at the end of the unit. Analysis of the results will be done considering the data as paired samples because each student took a pretest and a posttest.
False
True or False: A researcher wanted to see if there was an association between education attainment level and whether someone smokes or does not smoke. She classified education attainment into five categories: did not graduate from high school, high school graduate, some college, college graduate, or graduate degree, and then performed a chi-square test on the data. Her degrees of freedom are 10
False
True or False: A survey was conducted within city limits asking respondents if they were happy. Results, categorized by men/women, are below. The estimate of p, the pooled estimate, is 0.0649.
False
True or False: A teacher wants to compare the mean grades of his students to see if they differ at all. Given the following data summaries, we see that an analysis of variance test is more likely to reject the null hypothesis that the homework means are all equal because the four sample means for homework are farther apart than those for the quizzes. Mean assignment score for each student:
False
True or False: A tire manufacturer claims that one particular type of tire will last at least 50,000 miles. A group of angry customers do not believe this is so. They take a sample of 14 tires and want to test if the mean mileage of the tires is really 50,000. Thus, the customers want to test H0: μ = 50,000 versus Ha: μ ≠ 50,000.
False
True or False: A university professor wanted to know if the attitudes towards statistics changed during the course of the semester. She took a simple random sample of students and gave them a test at the beginning of the term to assess their feelings toward statistics. When the semester was finished, she administered another test to the same group of students and wanted to see if there was a difference between the average attitude toward statistics. Inference for these data will be based on a single random sample, because she only selected the students once.
False
True or False: ANOVA stands for analysis of variables.
False
True or False: About 13% of people in the United States are left-handed. One university planned a large 250-seat auditorium lecture hall with 15% "left-handed" seats. A class that filled the auditorium ran out of these seats because there were 18% left-handers in the class. The mean of the sampling distribution for the proportion of left-handers in the class should be 15%
False
True or False: About 13% of people in the United States are left-handed. One university planned a large 250-seat auditorium lecture hall with 15% "left-handed" seats. A class that filled the auditorium ran out of these seats because there were 18% left-handers in the class. The mean of the sampling distribution for the proportion of left-handers in the class should be 18%.
False
True or False: An assumption for creating a confidence interval for the difference of two means when the samples are small is that σ1 = σ2.
False
True or False: An experiment on the effectiveness of gingko biloba in helping boost memory function randomly assigned half the subjects to gingko and the other half to a placebo. At the end of the study, a 95% confidence interval for the difference in mean scores (gingko - control) on a memory function test is (-2.34, 4.39). Because the interval contains 0, we cannot make a decision about gingko based on this study.
False
True or False: An experiment on the effectiveness of gingko biloba in helping boost memory function randomly assigned half the subjects to gingko and the other half to a placebo. At the end of the study, a 95% confidence interval for the difference in mean scores (gingko - control) on a memory function test is (-2.34, 4.39). Because the interval has more positive values in it, gingko does help with memory function.
False
True or False: An experiment was conducted to see if elderly patients had more trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups. If we wanted to test whether the younger patients had less average forward/backward sway, we would use H0: μelderly = μ young versus Ha: μelderly ≠ μyoung.
False
True or False: An experiment was conducted to see if elderly patients had more trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups. This is an example of a matched pairs experiment because we are analyzing the mean difference between the elderly and the young
False
True or False: Are trees distributed randomly in a forest? A sample of 100 trees in the Wade tract was taken, and the tract divided into four equal parts. We test H0: pi = 1/4. The observed data are The chi-square test statistic is 10.28, P = 0.0163. At the 0.05 significance level, we conclude that trees are randomly distributed through the forest.
False
True or False: Because the analysis of variance F test is robust and provided the sample sizes are large enough, we can still make valid conclusions from the test results even when the samples are not randomly selected from the populations being compared.
False
True or False: Below is a table showing the results of a simple random sample asking respondents what types of cars they drive and their commuting distance to work in miles. If we reject the chi-square test null hypothesis, that means there is a difference in commuting distances for compact and mid-size car drivers.
False
True or False: Below is a table showing the results of a simple random sample asking respondents what types of cars they drive and their commuting distance to work in miles. This table has 15 cells.
False
True or False: Bill is doing a study comparing two groups with 99% confidence level and a 0.2 margin of error or less. He told his assistant that a sample size of 95 is the minimum needed for each group.
False
True or False: Chi-square distributions are left-skewed.
False
True or False: Drug sniffing dogs must be very accurate. Police do not want the dog to miss alerting them to drugs, nor do they want false alarms. Snuffy is in training. He correctly signaled 50 times out of 50 trials. Because he was 100% correct here, we cannot compute a confidence interval for his proportion of correct signals.
False
True or False: If X is the number of individuals in a sample that have the desired characteristic, the sample proportion is p^ = X.
False
True or False: If you increase the acceptable margin of error from 0.02 to 0.03, the required sample size will either increase or decrease because the sample sizes vary according to chance.
False
True or False: In ANOVA, the response variable is the categorical variable that is measured on each experimental unit.
False
True or False: In a sample of 592 college students, 457 said they make a point to practice "green" habits by recycling and purchasing low-carbon impact products when possible. The sample proportion p^ from this sample is 1.295.
False
True or False: In many comparison studies, there is more than one way to classify the populations. Analyzing the effects of two factors together requires the use of one-way ANOVA.
False
True or False: Jake hypothesizes that, in California, homes sell for significantly higher in May than in August. He also believes both months to have the same variance if they are within the same calendar year. He looked at a sample of 250 homes which sold in May versus 300 homes which sold in August of the same year. He found the May sold homes to have a mean sale price of $614,000 with a sample standard deviation of $28,000. He found the mean sales price of homes in August to be $608,000 with a standard deviation of $22,000. The pooled estimator of σ is $24,726.
False
True or False: Jessica believes that her 2-hour typing class is so good that she can improve senior citizen's speed significantly in the short amount of time. 15 senior citizens come to her class and she tests their wpm before and after her course. Using the sign test & the Normal approximation to Binomial, Jessica's p-value value for this analysis is 0.0469 (4 decimal places) and the null hypothesis is rejected.
False
True or False: Most people are concerned with green initiatives - use less, recycle, etc. Some people are installing rain barrels to catch run-off from rain on the roof of their homes for use in lawn and garden watering. Does this really change their metered water use? Members of one environmental group suggested installing the rain barrels on several homes and comparing water use this year to last year with a two-sample t test. This is a good idea because we will have data on both years' metered water use.
False
True or False: People theorize that getting married makes people more responsible. That's part of the reason married individuals have lower automobile insurance rates. Do married people also earn more? We plan to take a random samples of 100 married and 100 single people, and ask them their incomes. The hypotheses of interest are H0: μmarried = μsingle versus Ha: μmarried ≠ μsingle.
False
True or False: Suppose you want to estimate the proportion of adults in Vermont (population 0.6 million) that approve of the new health care bill. You also want to estimate the proportion of adults in New York (population 19 million) that approve of the new health care bill. To achieve the same margin of error in a 95% confidence interval for p in Vermont and New York, the required sample size of the Vermont sample will be smaller than the New York sample.
False
True or False: Suppose you want to estimate the proportion of students at a large university that approve of the new health care bill. From an SRS of 1000 university students, 778 approve of the health care bill. The margin of error for a 99% confidence interval for p is 0.013
False
True or False: The ANOVA model requires that all the sample sizes must be equal.
False
True or False: The M&M's candy company says that the distribution of colors for milk chocolate M&M's is and any variation from this distribution is solely due to imperfect packaging equipment. We opened a package and found 54 candies with the following counts of colors: The color that contributes least to the statistic is red.
False
True or False: The Model for one-way ANOVA requires each of the populations have a Normal distribution with the same mean.
False
True or False: The critical value for a 90% confidence interval when there are n = 10 observations is 1.812
False
True or False: The expected count for a cell in a two-way table is the grand total divided by the row total.
False
True or False: The goodness of fit test can only be used to see if each category of the variable is equally likely.
False
True or False: The supervisor of a fish hatchery needs to measure the length of a particular species every week to track their growth and verify that they maintain the mean length for that species for their age. She randomly selects 100 fish and measures their individual lengths in inches. The supervisor will not be able to conduct inference about the mean length this week because the data include two outliers.
False
True or False: The test statistic for the data below is -0.44.
False
True or False: There is longstanding belief that taking birth control pills might cause women to gain weight. A study on how birth control pills might affect basal metabolism found that the average basal metabolism rate from n = 24 women who had used oral contraceptives at least six months was 5841 kilo Joules per day (kJ/d) and the average basal metabolism rate from n = 22 women who had never used birth control was 5633 kilo Joules per day (kJ/d) (Diffey, Piers, Soares, and O'Dea. "The effect of oral contraceptive agents on the basal metabolic rate of young women." British Journal of Nutrition. June 1997.) Inference using two-sample t procedures and the conservative degrees of freedom will have 44 degrees of freedom.
False
True or False: Under the assumptions of ANOVA, a sample contrast has an F distribution.
False
True or False: When an opinion poll states with 95% confidence the margin of error for the sample percentage is plus or minus 3 percentage points, this means that the percentage of people who said "Yes" to the question was between 92% and 98%.
False
True or False: When determining the P-value, the F test may be two-sided or one-sided depending on the alternative hypothesis.
False
True or False: You may use a two sample t-test in the following situation: n1 = 10 and n2 = 10, data is close to Normal, 3 outliers present. Content_hint: Guidelines for the one-sample t procedures remain the same for two sample procedures, except the sample size of interest is now n1 + n2.
False
True or false: In a two-sample problem, if the response variable is categorical, we compare means.
False
True or false: In a two-sample problem, if the response variable is quantitative, we compare proportions
False
Suppose there are three distinct routes that connect your home to school. Every morning, you roll a die to randomly choose which of the three routes you will use that day. You record the amount of time it takes to commute to school to test whether there is a significant difference in the mean amount of time each route takes. You conduct this experiment twice. The results of both experiments are displayed in the following boxplots: Which set of data is more likely to reject the null hypothesis of an analysis of variance test?
Figure A, because there is much less variation among the times for each route.
A sociologist is interested in determining if the mean GPA is the same for students in all four undergraduate class levels. Assume all populations are normally distributed and all population variances are equal. What is the response variable?
GPA
One of the selling points of golf balls is their durability. An independent testing laboratory is commissioned to compare the durability of four different brands of golf balls. To measure durability, the number of hits required until the outer covering cracks is recorded for each ball. Which of the following are the experiment units?
Golf Balls
A researcher is interested in the physical fitness level of boys in different grade levels. She collects physical fitness scores for boys in kindergarten, 2nd grade, 4th grade and 6th grade. She is interested in performing a one-way ANOVA to determine if there is a difference in the mean physical fitness score for the four grade-levels. What is the factor?
Grade level
A randomized, double blind clinical study was conducted on adults aged 50 to 59 to test the effectiveness of a new vaccine for shingles (skin blisters caused by a virus). Approximately, half of the participants were randomly assigned to the vaccine group and the rest to the placebo group. Participants were monitored for at least a year after receiving either the vaccine or the placebo for occurrence of shingles. Those who developed the new vaccine want to show that the proportion of those who get shingles is less for those receiving the vaccine than those who don't. Letting those who receive the vaccine be treatment 1 and those receiving the placebo be treatment 2, what are the appropriate hypotheses for this test?
H0: p 1 = p2 versus Ha: p1 < p2
A survey was conducted on religious practices in the United States. Among other questions, respondents were asked their gender and whether they prayed at least once a day. Researchers suspect that women are more religious than men and want to test whether the proportion of women who pray at least once a day exceeds the proportion of men. Considering women to be population 1 and men to be population 2, what are the appropriate hypotheses for this test?
H0: p 1 = p2 versus Ha: p1 > p2
In a survey of college students at a large university, students were asked their gender and whether they liked country music. In analyzing these data, the researchers tested whether the proportions of males and females who like country music are significantly different. Considering males to be population 1 and females to be population 2, what are the appropriate hypotheses for this test?
H0: p 1 = p2 versus Ha: p1 ≠ p2
A shipment of 20,000 bags of oranges arrives at a distribution center with a nominal weight of 3200 g per bag. A sample of 10 bags is selected and weighed. The auditor wishes to test the hypothesis that the average weight of the cartons matches the nominal value vs. that the cartons are overweight at α = 0.05. Here is some computer output on the analysis of this data. Which are the null and alternate hypotheses?
H0: u=3200; H:u>3200
The supervisor of a fish hatchery measures the length of a particular species every week after hatching to track their growth. If their average length is too short or too long, they are not maturing properly and further tests must be done to determine the cause. She randomly selects 30 fish from among those that hatched five weeks ago and measures their individual lengths in inches to determine if they have grown to an average length of 9.7 inches. She observes an average length of 10.1 inches among the sample. What set of hypotheses is she interested in testing?
H0: μ = 9.7 versus Ha: μ ≠ 9.7
An experiment was conducted to see if elderly patients had more trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups. If we wanted to test whether the younger patients had less average forward/backward sway, we would use which of the following hypotheses?
H0: μ elderly = μ young versus Ha: μ elderly > μyoung
People theorize that getting married makes people more responsible. That's part of the reason married individuals have lower automobile insurance rates. Do married people also earn more? We plan to take a random samples of 100 married and 100 single people, and ask them their incomes. The hypotheses of interest are
H0: μmarried = μsingle versus Ha: μmarried > μsingle
Is the average rent for a two-bedroom apartment more than the average rent for a one-bedroom apartment? A sample of 10 advertisements of each type was collected, the rent (in dollars) for each suite was found, and the following is computer output of the analysis:
H0:u1=u2; H: u1<u2
Which of the following is true regarding the condition for ANOVA inference that all populations must have the same standard deviation σ?
If the largest sample standard deviation is no more than twice as large as the smallest one, the condition is considered to be satisfied.
Can scented coupons increase sales? Three different coupons for juice were mailed to households - U (unscented), A (apple scented), and C (citrus scented). The number of cartons of the juice purchased with each type of coupon was measured at a store. The following is the output from an analysis of the experiment: Which of the following is correct?
If the population means were equal, the observed data is highly unusual.
The Motion Picture Association of America (MPAA) gives every movie a rating to indicate the appropriate audience. Ratings include G for general audience, PG for parental guidance, and PG-13 for audiences at least 13 years of age. A researcher wants to determine if the mean running time of movies is the same for each rating. What is the factor?
Movie Rating
A train operator claims that they are never more than seven minutes late. A commuter takes a simple random sample of trains arriving at her local station of size n = 19 and records their estimated arrival time and the actual arrival time. She creates the following stemplot for these data. 4 | 9 5 | 045699 6 | 0023444 7 | 357 8 | 05 Based on the stemplot, she should continue with her use of the t procedure because even though the sample size is small, the data look roughly ________.
Normal
One of the conditions for inference about a mean states that the population values have a _______ distribution.
Normal
To be able to conduct an analysis of variance procedure, we assume that each of the populations being compared has a/an ________ distribution.
Normal
We check np^ ≥ and n(1 - p^) ≥ 15 when doing a confidence interval for p to check that the sample size is large enough for the sampling distribution of p^ to be approximately ___________.
Normal
Under the assumptions of ANOVA, a sample contrast has what distribution?
Normal Distribution
A teacher wants to compare the mean grades of his students to see if they differ at all. Given the following data summaries, which set of assignments is more likely to reject the null hypothesis of an analysis of variance test? Mean assignment score for each student:
Quizzes, because compared to the variation within each group, the four sample means are far apart.
A sociologist is interested in determining if the mean GPA is the same for students in all four undergraduate class levels. Assume all populations are normally distributed and all population variances are equal. She wishes to test the following hypotheses to determine if there is evidence that the mean GPA differs. 𝐻𝑜:𝜇1=𝜇2=𝜇3=𝜇4 Ha: At least one class level has a different mean GPA. If the ANOVA F test yields P < 0.0001. What should we conclude?
Reject Ho and conclude there is sufficient evidence the mean GPA differs for the four undergraduate class levels.
The ANOVA idea is to break the total variation in the responses into two parts: the variation due to differences among the group means and that due to differences within groups. What does SSG stand for?
Sum of squares for groups
One of the selling points of golf balls is their durability. An independent testing laboratory is commissioned to compare the durability of four different brands of golf balls. To measure durability, the number of hits required until the outer covering cracks is recorded for each ball. Which of the following is the factor?
The brand of golf ball
Can scented coupons increase sales? Three different coupons for juice were mailed to households - U (unscented), A (apple scented), and C (citrus scented). The number of cartons of the juice purchased with each type of coupon was measured at a store. The ANOVA p-value was < 0.001. The study concluded in its report, "There was strong evidence from the ANOVA that the individual purchases made by recipients of scented coupons were larger than the purchases in the two other groups (p < 0.0001)." Which of the following is correct?
The conclusion is wrong because ANOVA tests for equality of means and not individual scores
Jessica believes that her 2-hour typing class is so good that she can improve senior citizen's speed significantly in just one class. 10 senior citizens come to her class and she tests their wpm before and after her course. To use the sign test & under the null hypothesis, she would assume ___________.
The data is distributed Binomial(n=10,p=0.5)
The ANOVA model which of the following is an assumption about the deviations εij?
The deviations εij are independent.
A study was conducted on caffeine consumption by children. The parents of 104 children aged 5-7 and 97 children aged 8-12 were surveyed about whether their child consumed caffeine. For the 5-7 year old children, 73% consumed caffeine and 80% of the 8-12 year old children consumed caffeine. A 95% confidence interval for the difference between the proportion of all 8-12 year olds who consume caffeine and the proportion of 5-7 year olds who consume caffeine was found to be (-0.05, 0.19). Which of the following is the correct interpretation of this interval?
The interval (-0.05, 0.19) gives a range of reasonable values for the difference between the proportions of all children who consume caffeine in the two age groups
In the Model for one-way ANOVA, what does xij represent?
The jth observation from the ith population.
Which of the following is correct?
The matched pair t-test is the same as the one-sample t-test but done on the differences.
Can scented coupons increase sales? Three different coupons for juice were mailed to households - U (unscented), A (apple scented), and C (citrus scented). The number of cartons of the juice purchased with each type of coupon was measured at a store. The following is the output from an analysis of the experiment. The following is a side-by-side boxplot of the individual purchases.Which of the following is correct?
The median score of the citrus and unscented groups are not displayed because they must be equal to either the 25th or 75th percentiles.
One of the selling points of golf balls is their durability. An independent testing laboratory is commissioned to compare the durability of four different brands of golf balls. To measure durability, the number of hits required until the outer covering cracks is recorded for each ball. Which of the following is the response variable?
The number of hits required until the outer covering cracks
A shipment of 20,000 bags of oranges arrives at a distribution center with a nominal weight of 3200 g per bag. A sample of 10 bags is selected and weighed. The auditor wishes to test the hypothesis that the average weight of the cartons matches the nominal value vs. that the cartons are overweight at α = 0.05. Here is some computer output on the analysis of this data. Which of the following is correct?
The p-value is 0.02 and there is evidence at α = 0.05 that the mean weight is greater than the nominal weight.
In the Model for one-way ANOVA, what does s2p represent?
The pooled sample variance.
Which of the following conditions is not necessary to conduct inference about a population mean?
The population standard deviation must be known.
Can scented coupons increase sales? Three different coupons for juice were mailed to households - U (unscented), A (apple scented), and C (citrus scented). The number of cartons of the juice purchased with each type of coupon was measured at a store. The ANOVA p-value was < 0.001.Which of the following is correct?
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.
Can scented coupons increase sales? Three different coupons for juice were mailed to households - U (unscented), A (apple scented), and C (citrus scented). The number of cartons of the juice purchased with each type of coupon was measured at a store. The following is a normal quantile plot and a plot of the residuals from an analysis of the experiment:Which of the following is correct?
The standard deviation within the groups is about 0.75.
Is the average rent for a two-bedroom apartment more than the average rent for a one-bedroom apartment? A sample of 10 advertisements of each type was collected and the rent (in dollars) for each suite was found. Here are some preliminary statistics: Which of the following is correct?
The standard errors measure how much the average rent for each class could vary if new samples of size 10 were taken.
Can scented coupons increase sales? Three different coupons for juice were mailed to households - U (unscented), A (apple scented), and C (citrus scented). The number of cartons of the juice purchased with each type of coupon was measured at a store. The ANOVA p-value was < 0.0001. Here are the results of a multiple comparison method following an ANOVA: Which of the following is correct?
There is insufficient evidence to distinguish the population means of the citrus and apple scented groups.
A randomized, double blind clinical study was conducted on adults aged 50 to 59 to test the effectiveness of a new vaccine for shingles (skin blisters caused by a virus). Approximately, half of the participants were randomly assigned to the vaccine group and the rest to the placebo group. Of the 11228 receiving the placebo, 99 or 0.0088 got shingles. Of the 11,211 receiving the vaccine, 30 or 0.0027 got shingles. Using SE = 0.001008, a 99% confidence interval was found to be (0.0088 - 0.0027) ± (2.576)(0.001008) or (0.0035, 0.0087). True or false: The 99% confidence interval (0.0035, 0.0087) estimates the difference between the proportion of all 50 to 59 year old adults receiving a placebo who will get shingles and the proportion of all 50 to 59 year old adults receiving a vaccine who will get shingles
True
A survey was conducted on religious practices in the United States. Among other questions, respondents were asked their gender and whether they prayed at least once a day. Of the 19,271 females, 66% said they prayed at least daily and of the 16,285 males, 49% said they prayed at least daily. Use SE = 0.0052 and carry 3 decimal places. True or false: A 95% confidence interval for the difference in the proportion of females who pray at least once a day and the proportion of males who pray at least once a day is (0.160, 0.180).
True
A survey was conducted on religious practices in the United States. Among other questions, respondents were asked their gender and whether they prayed at least once a day. Of the 19,271 females, 66% said they prayed at least daily and of the 16,285 males, 49% said they prayed at least daily. Using SE = 0.0052, a 95% confidence interval was found to be (0.66 - 0.49) ± (1.960)(0.0052) or (0.160, 0.180). True or false: The 95% confidence interval (0.160, 0.180) estimates the difference between the proportion of all women who pray at least once a day and the proportion of all men who pray at least once a day.
True
An essential requirement of models for two-way tables is that each experimental unit or subject is counted only once in a data table.
True
In a survey of college students at a large university, students were asked their gender and whether they liked country music. Of the 189 females, 68.3% like country music. Of the 155 males, 45.8% like country. True or false: A 90% confidence interval for the difference in the proportion of the female students who like country and the proportion of the male students like country music is (0.139, 0.311). (Use SE = .0524, and carry 3 decimal places.)
True
In a survey of college students at a large university, students were asked their gender and whether they liked country music. Of the 189 females, 68.3% like country music. Of the 155 males, 45.8% like country. Using SE = .0524, a 90% confidence interval was found to be (0.683 - 0.458) ± (1.645)(0.0524) or (0.139, 0.311). True or false: The 95% confidence interval (0.139, 0.311) estimates the difference between the proportion of all women at this university who like country and the proportion of all men at this university who like country.
True
This question requires a graphing calculator or software. True or False: Theoretically, regular exercise makes the heart pump more efficiently, so normally it would not have to beat as often. A researcher wants to examine this effect in a population of college-age students. The resting heart rates for 20 students who exercise regularly had mean 63.2 beats per minute and standard deviation 5.3 beats per minute. The resting heart rates for 25 students who do not exercise regularly had mean 73.4 beats per minute and standard deviation 8.9 beats per minute. Based on these samples, we can say that regular exercise in college-age people decreases the resting heart rate by an average of 5.02 to 15.35 beats per minute, with 98% confidence.
True
True or False: There is longstanding belief that taking birth control pills might cause women to gain weight. A study on how birth control pills might affect basal metabolism found that the average basal metabolism rate from n = 24 women who had used oral contraceptives at least six months was 5841 kilo Joules per day (kJ/d) and the average basal metabolism rate from n = 22 women who had never used birth control was 5633 kilo Joules per day (kJ/d) (Diffey, Piers, Soares, and O'Dea. "The effect of oral contraceptive agents on the basal metabolic rate of young women." British Journal of Nutrition. June 1997.) The authors reported P = 0.002 for the results of the t test comparing the two basal metabolism rates. We will decide to reject H0 because the P-value is small. There is a difference in the mean metabolism rates for women who take birth control pills and those who don't. From the given means, it appears that women who take the Pill have a higher basal metabolism rate, on average.
True
True or False: A group of psychologists was interested in knowing if living environment had any effect on a student's grade point average (GPA). They took a set of twins and randomly assigned one twin to live in an urban area and the other twin to live in a rural area. After one year, they computed the GPAs for the twins and looked at the differences. The psychologists found the mean difference in the GPAs between the 24 sets of twins was 0.11 with standard deviation 0.24. The test statistic for a test of whether a significant difference between GPAs exists is 2.198.
True
True or False: A reasonable design for an experiment to evaluate a new teaching method might be to have all the students take a pretest, randomly assign half to the new method and half to the standard method, then have all students take a test at the end of the unit. Analysis of the results will be done considering the data as independent samples because there were two groups of students.
True
True or False: A statistics teacher was interested in looking at the possible effects that working for pay had on her students. One question she was interested in was how many hours students work for pay, since that could have an impact on the time available for studying. She asked a sample of students to fill out a questionnaire about their study and work habits. Some of the results are shown below. Half the male students in this sample don't work for pay.
True
True or False: A university professor wanted to know if the attitudes towards statistics changed during the course of the semester. She took a simple random sample of students and gave them a test at the beginning of the term to assess their feelings toward statistics. When the semester was finished, she administered another test to the same group of students and wanted to see if there was a difference between the average attitudes toward statistics. This study has a matched pairs design.
True
True or False: About 13% of people in the United States are left-handed. One university planned a large 250-seat auditorium lecture hall with 15% "left-handed" seats. A class that filled the auditorium ran out of these seats because there were 18% left-handers in the class. The mean of the sampling distribution for the proportion of left-handers in the class should be 13%
True
True or False: An analysis of two rival airports was completed. The number of flights with a full passenger list are recorded below. The difference in proportions is statistically significant, based on a 95% confidence level.
True
True or False: An experiment on the effectiveness of gingko biloba in helping boost memory function randomly assigned half the subjects to gingko and the other half to a placebo. At the end of the study, a 95% confidence interval for the difference in mean scores (gingko - control) on a memory function test is (-2.34, 4.39). Based on this information, we can conclude that because the interval contains 0, it is reasonable that there is no difference in average memory function between people who take gingko and those who do not.
True
True or False: An experiment was conducted to see if elderly patients had more trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups. If we wanted to test whether the younger patients had less average forward/backward sway, we would use H0: μelderly = μ young versus Ha: μelderly > μyoung
True
True or False: An experiment was conducted to see if elderly patients had more trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups. The researchers conducted the experiment and obtained data summarized in the following table: The standardized test statistic is 2.30.
True
True or False: How does seat belt use vary with drivers' race or ethnic group? The answer depends on gender (males are less likely to buckle up) and also on location. Here are data on a random sample of male drivers observed in Houston: The number of unbelted blacks was 96.
True
True or False: If the null hypothesis H0: p = p0 is true, p0 is the mean of the sampling distribution of p^.
True
True or False: If you increase the acceptable margin of error from 0.02 to 0.03, the required sample size will decrease.
True
True or False: In ANOVA, a factor is the categorical explanatory variable that classifies the populations.
True
True or False: In a completely randomized experimental design, all the subjects are allocated at random among all the treatments and their responses are observed.
True
True or False: Most people are concerned with green initiatives - use less, recycle, etc. Some people are installing rain barrels to catch run-off from rain on the roof of their homes for use in lawn and garden watering. Does this really change their metered water use? Members of one environmental group suggested installing the rain barrels on several homes and comparing water use this year to last year with a two-sample t test. This is not a good idea because weather patterns might be different this year than last.
True
True or False: Multiple-comparisons methods are commonly used only after rejecting H0.
True
True or False: People theorize that getting married makes people more responsible. That's part of the reason married individuals have lower automobile insurance rates. Do married people also earn more? We plan to take a random samples of 100 married and 100 single people, and ask them their incomes. The hypotheses of interest are H0: μmarried = μsingle versus Ha: μmarried > μsingle
True
True or False: Small samples create a particular difficulty for statistical analysis because the power of the statistical tests are usually low
True
True or False: Suppose we are interested in testing H0: p = p0 versus Ha:p ≠ p0. p0 is the hypothesized proportion
True
True or False: Suppose you want to estimate the proportion of adults in Vermont (population 0.6 million) that approve of the new health care bill. You also want to estimate the proportion of adults in New York (population 19 million) that approve of the new health care bill. To achieve the same margin of error in a 95% confidence interval for p in Vermont and New York, the required sample size of the Vermont sample will be the same as the New York sample.
True
True or False: The critical value for a 70% confidence interval when there are n = 19 observations is 1.067.
True
True or False: The method of testing the equality of several means all at the same time, rather than using two-sample tests over and over again, is known as multiple comparisons.
True
True or False: The supervisor of a fish hatchery measures the length of a particular species every week after hatching to track their growth. If their average length is too short or too long, they are not maturing properly and further tests must be done to determine the cause. She randomly selects 30 fish from among those that hatched five weeks ago and measures their individual lengths in inches to determine if they have grown to an average length of 9.7 inches. She observes an average length of 10.1 inches among the sample. She is interested in testing H0: μ = 9.7 versus Ha: μ ≠ 9.7.
True
True or False: The t distributions have more spread than the standard Normal distribution
True
True or False: There is longstanding belief that taking birth control pills might cause women to gain weight. A study on how birth control pills might affect basal metabolism found that the average basal metabolism rate from n = 24 women who had used oral contraceptives at least six months was 5841 kilo Joules per day (kJ/d) and the average basal metabolism rate from n = 22 women who had never used birth control was 5633 kilo Joules per day (kJ/d) (Diffey, Piers, Soares, and O'Dea. "The effect of oral contraceptive agents on the basal metabolic rate of young women." British Journal of Nutrition. June 1997.) The authors reported P = 0.002 for the results of the t test comparing the two basal metabolism rates. We will decide to reject H0 because the P-value is small. There is a difference in the mean metabolism rates for women who take birth control pills and those who don't. From the given means, it appears that women who take the Pill have a higher basal metabolism rate, on average.
True
True or False: To be able to conduct an analysis of variance procedure, we assume that each of the populations being compared has a Normal distribution.
True
True or False: To calculate the confidence interval using the "Plus 4" or the Wilson methods, we add 4 trials, 2 of which are "successes", and 2 of which are "failures."
True
True or False: Using technology, a sample size of 230 is needed for a significance test that the two proportions are equal using a two-sided alternative with p1 =0.15 and p2 =0.27, α = 0.02, and 80% power.
True
True or False: We examine donors lined up randomly at a blood drive. We are interested in how many of them have type O blood. This is a situation where we will be interested in a population proportion.
True
True or False: When contrasts are formulated before seeing the data, inference about contrasts is valid whether or not the ANOVA null hypothesis of equality of means is rejected.
True
True or False: When we choose to use a matched pairs design, it is because the parameter of interest is μ, the population mean difference in the responses between the two groups receiving the treatments.
True
True or False: You want to estimate the proportion of students at your university in favor of a longer spring break. Changing the confidence level from 95% to 90% will make the necessary sample smaller if the margin of error stays the same.
True
True or false: All confidence intervals have the form: estimate ± z*SEestimate
True
True or false: The data used for comparing two proportions has a categorical explanatory variable with two levels and a categorical response variable with two levels.
True
True or false: The null hypothesis in a test of significance basically says that there is no difference between the two populations.
True
You have available data showing that 81% of all eligible students in Connecticut took the SAT during the 1994-1995 school year. You are interested in testing whether the proportion of eligible students in Connecticut that plan to take the SAT during 2010-2011 school year is significantly different than the proportion that took the SAT during the 1994-1995 school year. you take an SRS of size 1000 of Connecticut students eligible to take the SAT and find that 85% plan to take the SAT during the 2010-2011 school year. What is the region corresponding to the P-value for the test of hypothesis?
Two-sided
How much, on average, does rent for a two-bedroom apartment differ from rent for a one-bedroom apartment? A sample of 10 advertisements of each type was collected, the rent (in dollars) for each suite was found, and the following is computer output of the analysis: Which of the following is correct?
We are 95% confident that the average increase in rent is between about $0 and $160
Which of the following is not a benefit of using a matched pairs design?
We do not have to calculate the standard error of the mean difference when using inference procedures
Do students tend to improve their GMAT scores the second time they take the test? A random sample of 10 students who took the test twice was selected and the following output summarizes the results of an analysis of the differences (second score - first score): Assume that the changes in GMAT scores (second score - first score) have an approximate normal distribution. Which of the following is correct?
We have strong evidence at α = 0.05 that the mean score the second time around is greater than the mean score on the first test.
A randomized, double blind clinical study was conducted on adults aged 50 to 59 to test the effectiveness of a new vaccine for shingles (skin blisters caused by a virus). Approximately, half of the participants were randomly assigned to the vaccine group and the rest to the placebo group. Participants were monitored for at least a year after receiving either the vaccine or the placebo for occurrence of shingles. The following table summarizes these data: Those who developed the new vaccine want to show that the proportion of those who get shingles is less for those receiving the vaccine than those who don't. Letting those who receive the vaccine be treatment 1 and those receiving the placebo be treatment 2, the appropriate hypotheses for this test are: H0: p 1 = p2 versus Ha: p1 < p2 The p-value for this test is 0.0000 (to 4 decimal places). What are the appropriate conclusions at alpha = 0.05?
We reject H0 and conclude that the proportion of those receiving the vaccine who get shingles is significantly less than the proportion of those who don't.
When comparing several means, each of the following statements illustrates a benefit of performing an ANOVA test instead of the two-sample t test multiple times, except for which one?
We will get multiple P-values.
When do we use the t distribution to make inference about μ?
When we do not know μ or σ.
A randomized, double blind clinical study was conducted on adults aged 50 to 59 to test the effectiveness of a new vaccine for shingles (skin blisters caused by a virus). Approximately, half of the participants were randomly assigned to the vaccine group and the rest to the placebo group. Participants were monitored for at least a year after receiving either the vaccine or the placebo for occurrence of shingles. The following table summarizes these data: Are these sample sizes large enough for appropriately computing a large-sample confidence interval estimate for the difference between two population proportions?
Yes
A survey was conducted on religious practices in the United States. Among other questions, respondents were asked their gender and whether they prayed at least once a day. The following table summarizes these data: Are these sample sizes large enough for appropriately computing a large-sample confidence interval estimate for the difference between two population proportions?
Yes
A university professor wanted to know if the attitudes towards statistics changed during the course of the semester. She took a simple random sample of students and gave them a test at the beginning of the term to assess their feelings toward statistics. When the semester was finished, she administered another test to the same group of students and wanted to see if there was a difference between the average attitudes toward statistics. Does this study have a matched pairs design?
Yes
In a survey of college students at a large university, students were asked their gender and whether they liked country music. The following table summarizes these data: Are these sample sizes large enough for appropriately computing a large-sample confidence interval estimate for the difference between two population proportions?
Yes
Suppose there are three distinct routes that connect your home to school. Every morning, you roll a die to randomly choose which of the three routes you will use that day. You record the amount of time in minutes it takes to commute to school to test whether there is a significant difference in the mean amount of time each route takes. After one month, you summarize the data. Stemplots for the times from each of the three routes are roughly Normal. Does it seem that the conditions for ANOVA are met?
Yes
What does ANOVA stand for?
analysis of variance
If independent large samples are taken from two populations, the sampling distribution of the difference between the sample means
can be approximated by a Normal distribution.
The method of testing the equality of several means all at the same time, rather than using two-sample tests over and over again, is known as multiple ________.
comparisons
How does seat belt use vary with drivers' race or ethnic group? The answer depends on gender (males are less likely to buckle up) and also on location. Here are data on a random sample of male drivers observed in Houston: A bar graph to display these data will compare the _________ frequencies.
conditional
If you increase the acceptable margin of error from 0.02 to 0.03, the required sample size will
decrease
If you increase the acceptable margin of error from 0.02 to 0.03, the required sample size will ___________________.
decrease
As the ________ increase, the t density curve approaches the standard Normal curve.
degrees of freedom
The parameter/s associated with an F distribution is/are ________.
df1 and df2
The true benefit of using a matched pairs design is that we can simply look at the ________ within each pair and use one-sample inference procedures.
differences
We can still perform inference on non-Normal populations by using a _______ significance test
distribution-free test
Researchers performed a study on the effects of a nonsteroidal anti-inflammatory drug (NSAID) given before and after arthroscopic knee surgery. A sample of 67 patients undergoing elective knee arthroscopy was randomly divided into three treatment groups. Researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery. Using α = 0.05 and on the basis of the ANOVA computer output given above, the researchers conclude that there is significant evidence to suggest that the mean pain scores in the three treatment groups one day after surgery are not ________.
equal
In ANOVA, a _________ is the categorical explanatory variable that classifies the populations being compared.
factor
If the null hypothesis is false, the observed variability in the sample means will be ________ the variability you would expect if the means are equal.
greater than
As the degrees of freedom ________, the t density curve approaches the standard Normal curve.
increase
A paint manufacturer wants to compare drying times of two different types of paint. They use type A on a random sample of 12 walls and type B on a different sample of 12 walls. Comparing the mean drying times for the two types will involve a __________ samples test
independent
A reasonable design for an experiment to evaluate a new teaching method might be to have all the students take a pretest, randomly assign half to the new method and half to the standard method, then have all students take a test at the end of the unit. Final analysis of the results will be done considering the data as ______________ samples.
independent
In the model for examining independence in two-way tables, the null hypothesis is that the row and column variables are _______________.
independent
A reasonable design for an experiment to evaluate a new teaching method might be to have all the students take a pretest, randomly assign half to the new method and half to the standard method, then have all students take a test at the end of the unit. Analysis of the final results will be done considering the data as
independent samples because there were two groups of students
A group of psychologists was interested in knowing if living environment had any effect on a student's grade point average (GPA). They took a set of twins and randomly assigned one twin to live in an urban area and the other twin to live in a rural area. After one year, they computed the GPAs for the twins and looked at the differences. The psychologists calculated a 95% confidence interval for μ to be (−0.066, 0.146). Thus, we have ________ evidence to conclude at a significance level of α = 0.05 that there is a significant difference in GPA between living in a rural or urban area.
insufficient
The standard error
is an estimate, using sample data, of the standard deviation of the sampling distribution of p^.
In a two-sample problem, if the response variable is quantitative, do we compare means or proportions?
means
One-way analysis of variance is a statistical method for comparing several population ___________
means
The method of testing the equality of several means all at the same time, rather than using two-sample tests over and over again, is known as ________.
multiple comparisons
Suppose that we use a simple random sample of size n to estimate the mean commute time of students from their residence to campus. The histogram of the n commute times looks roughly symmetric but has one extremely large outlier. The robustness of our procedures will allow us to conduct inference in all of following cases except which one?
n = 10
Which of the following situations will you most likely NOT be able to use a two-sample t procedure?
n1 = 10 and n2 = 10, data is close to Normal, 3 outliers present
The data for one-way ANOVA are SRSs from each of the I populations being compared. What is the symbol for the number of observation in the sample that was selected from the ith population?
ni
If independent large samples are taken from two populations, the sampling distribution of the difference between the sample means will be approximately
normal
The supervisor of a fish hatchery needs to measure the length of a particular species every week to track their growth and verify that they maintain the mean length for that species for their age. She randomly selects 100 fish and measures their individual lengths in inches. The supervisor will able to conduct inference about the mean length this week because the data resembles a ________ distribution.
normal
Historically, returns on investments in the stock market are about 7% per year. A 7% return means a $1000 investment will be worth $1070 at the end of one year. The 7% figure is a ____________
not a proportion
Researchers performed a study on the effects of a nonsteroidal anti-inflammatory drug (NSAID) given before and after arthroscopic knee surgery. A sample of 83 patients undergoing elective knee arthroscopy was randomly divided into three treatment groups. Group 1 was given the drug before and after surgery. Group 2 was given a placebo before surgery and the drug after. Group 3 was given the placebo before and after surgery. Researchers compared the mean pain scores of the patients in the three treatment groups one day after surgery. The ________ for this study is that the true mean pain scores for the populations of all three groups are equal.
null hypothesis
What is the parameter for comparing two proportions?
p^1 - p^2
The correct interpretation of the test statistic t is that it says how many standard deviations the sample mean is away from the ________. (This is a two word answer.)
population mean
Small samples create a particular difficulty for statistical analysis because the _______ of the statistical tests are usually low.
power
In ANOVA, the _________ is the quantitative variable that is measured on each experimental unit
response
The shape of all the F distributions is ________.
right-skewed
He can use a t-test here because at a sample size of n1 + n2 >40, the t-procedure is _______ to potential Non-normality and outliers that may exist in the sample. Content_hint: Guidelines for the one-sample t procedures remain the same for two sample procedures, except the sample size of interest is now n1 + n2.
robust
To say that our inference procedures are ________ means that the confidence level or P-value does not change very much when certain conditions of inference are violated
robust
Expected counts in a two-way table are (_______) total x (column total) / (table total).
row
When the value of the population standard deviation is unknown, we estimate it with ________ to conduct inference about a population mean.
s
We use the t distribution to make inference about μ when we do not know μ or ________ from the population.
sigma
You want to estimate the proportion of students at your university in favor of a longer spring break. Changing the confidence level from 95% to 90% will make the necessary sample size ________ if the margin of error stays the same
smaller
The __________ is an estimate, using sample data, of the standard deviation of the sampling distribution of p^.
standard error
To estimate σ/√n, the true variation of x̄, we use s/√n which is known as the ________ of x̄. (This is a two word answer.)
standard error
Which distribution has greater spread?
t
When comparing several means, a weakness of performing the two-sample ________ multiple times instead of an ANOVA test is that we will get multiple P-values
t-test
This question requires a graphing calculator or software. True or False: Theoretically, regular exercise makes the heart pump more efficiently, so normally it would not have to beat as often. A researcher wants to examine this effect in a population of college-age students. The resting heart rates for 20 students who exercise regularly had mean 63.2 beats per minute and standard deviation 5.3 beats per minute. The resting heart rates for 25 students who do not exercise regularly had mean 73.4 beats per minute and standard deviation 8.9 beats per minute. Based on these samples, we can say that
the average resting heart rate for college-age individuals who exercise is less than the average resting heart rate for college-age individuals who do not exercise
The purpose of a confidence interval for p is __________.
to give a range of reasonable values for the population proportion
The National Park Service is interested in comparing the amount of money that visitors in two different national parks spend. They sample visitors on the same day in each of the two parks and then compare the mean dollar amounts spent from each sample. Analysis for these data will be based on a _____-sample design.
two
The National Park Service is interested in comparing the amount of money that visitors in two different national parks spend. They sample visitors on the same day in each of the two parks and then compare the mean dollar amounts spent from each sample. Analysis for these data will be based on
two independent samples
An experiment was conducted to see if elderly patients had more trouble keeping their balance when loud, unpredictable noises were made compared to younger patients who were also exposed to the noises. Researchers compared the amount of forward and backward sway for the two groups. To analyze the data, we will use a ________ t test
two-sample
You have available data showing that 81% of all eligible students in Connecticut took the SAT during the 1994-1995 school year. You are interested in testing whether the proportion of eligible students in Connecticut that plan to take the SAT during 2010-2011 school year is significantly different than the proportion that took the SAT during the 1994-1995 school year. you take an SRS of size 1000 of Connecticut students eligible to take the SAT and find that 85% plan to take the SAT during the 2010-2011 school year. The region corresponding to the P-value for the test of hypothesis is _____________.
two-tailed
Which of the following gives a confidence interval for the population mean when the population standard deviation is not known?
± t* s/√n
Which of the following is not a required assumption for creating a confidence interval for the difference of two means when the samples are small?
σ1 = σ2