all STP questions known

A regression equation was constructed relating the time spent studying for an exam (X) and the score received on the first exam (Y) for 25 students in a calculus course. The y-intercept was found to be 95 while the slope was found to be -0.8. In addition, the coefficient of determination was calculated to be 60.0%. What is the correlation coefficient between X and Y in this problem (rounded to 2 decimal places)?

-0.77

Find the P-value for the indicated hypothesis test. In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a hypothesis test to determine whether the proportion of all adults in the town that have been exposed to this strain of the flu differs from 8%.

0.0048 null hypothesis = p = .08

Find the value of (alpha) that corresponds to a level of confidence of 96%

0.04

For a t-curve with df = 4, find t0.05

2.132

For a t-curve with df = 4, find t0.05. (that is, find a t value with subscript of alpha = 0.05)

2.132

The partially filled contingency table gives the relative frequencies of the data on age (in years) and sex from the residents of a retirement home. Age (yrs) What percentage of residents are males in the age group 60-79?

29%

The time to complete a certain task was recorded for 7 people with times of (in minutes): 2, 1, 2, 7, 5, 5, 6 What is the median time to complete this task?

5

Find the sample median for the following set of data: 26, 20, 100, 51, 54, 14, 73, 48, 53, 60, 66, 43, 71

53

Here is a histogram for a set of test scores from a 10-question makeup quiz given to a group of students who were absent on the day the quiz was given. What percent of students received scores less than 4?

80%

What condition would you need to know in order to say that a change in the variable X causes a change in the variable Y? (There is only 1 correct answer)

A designed experiment reveals that a change in X causes a change in Y.

A two-sample t test is going to be carried out where it is assumed that the population variances are unknown but assumed equal. The first sample of 30 items were chosen and measured. For this first sample, an average response of 125 with a sample variance of 25 was found. The second sample of 40 items were chosen and measured. This second sample had an average response of 132 with a sample variance of 16. What is the pooled standard deviation for this problem? (rounded to second place after the decimal)

A. 4.45

Which of the following two graphs has the higher standard deviation?

B has higher than A

The following output from a two-sample t-test using Minitab was obtained for a particular problem: Two-sample T for side_side Age_Group N Mean StDev SE Mean elderly 9 22.2 10.3 3.4 young 8 15.13 3.91 1.4 Difference = mu (elderly) - mu (young) Estimate for difference: 7.10 95% CI for difference: (-1.13, 15.32) T-Test of difference = 0 (vs not =): T-Value = 1.92 P-Value = 0.083 DF = 10 For which of the following levels of significance would you reject the null hypothesis?

C. 0.10

A sample mean, sample size, and population standard deviation are given. Use the P-value appraoch to perform a one-mean z-test about the mean, μ, of the population from which the sample was drawn. Determine the strength of the evidence against the null hypothesis.

C. z = 1.57; P-value = 0.1164; Do not reject H0. The evidence against the null hypothesis is weak or none.

Fifteen people will be enrolled in a four-week foreign language course. On the first day, the instructor gives the students an exam to determine how much they already know. At the end of the four weeks, the instructor gives the students the same exam again. From the exam scores, the instructor wants to determine if taking the course has significantly increased the students' foreign language ability. Which of the four cases in Chapter 10 does this problem fall under or represent?

Case IV

A hypothesis test for a population mean is to be performed at the 5% level of significance. The population standard deviation is known. The hypotheses are H0: μ = 80 Ha: μ ≠ 80. A 95% confidence interval for μ is also constructed. True or false, if 80 lies within the 95% confidence interval, then the null hypothesis will be rejected

false

According to the U.S. Bureau of Labor Statistics, self-employed persons with home-based businesses work an average of 23 hours per week at home. Which of the following 95% two-sided confidence intervals on the true average number of hours worked per week at home would support the U.S. Bureau of Labor Statistics reported average of 23 hours per week at home.

(21.449, 25.332)

The time to repair an electronic device is a normally distributed random variable measured in hours. It is believed that the true average time to repair such a device is 225 hours. Which of the following 95% confidence intervals would lead to rejecting the claim that the average time to repair the devices is 225 hours?

(236.77, 241.82)

An experimenter wants to conduct a hypothesis test on a claim that there was no difference between two population means. That is, H0: μ1 - μ2 = 0. Which of the following 95% confidence intervals on the difference, μ1 - μ2, would lead to rejection of the null hypothesis at the 5% level of significance?

(3.5, 5.6)

Use the two-proportions z-interval procedure to obtain the required confidence interval for the difference between two population proportions. Assume that independent simple random samples have been selected from the two populations. A survey of students at one college found that 57 of 96 randomly selected freshmen and 85 of 118 randomly selected sophomores lived off campus. Find a 98% confidence interval for the difference between the proportions of freshmen and sophomores at this college who live off campus.

-0.278 to 0.025

Use the paired t-interval procedure to obtain the required confidence interval. You may assume that the conditions for using the procedure are satisfied. A test of abstract reasoning is given to a random sample of students before and after completing a formal logic course. The results are shown below. Before After Determine a 95% confidence interval for the difference between the mean score before completing the course and the mean score after completing the course.

-1.6 to 6.0

Use the standard normal curve find the value of z when the area to its left is 0.04

-1.75

Estimate the probability of the event. In a certain class of students, there are 10 boys from Wilmette, 5 girls from Kenilworth, 10 girls from Wilmette, 7 boys from Glencoe, 5 boys from Kenilworth and 6 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth?

.233

The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?

0.0166

The average weight of a certain part manufactured by a company is 15 kg with a standard deviation of 0.6 kg. If 36 of these parts are randomly selected, what is the probability the average weight will be at least 15.2 kg?

0.0228

Suppose that D is a random variable. Given that P(D > 4.4) = 0.95, find P(D 4.4).

0.05

A brand of water softener salt comes in packages marked "net weight 40 lbs". The company that packages the salt claims that the bags contain an average of 40 lb. of salt and that the standard deviation of the weights is 0.6 lb. assume that the weights are normally distributed. For samples of size 36, find the standard deviation of the distribution of all possible sample mean weights (i.e., find the standard error of all possible sample mean weights).

0.1

Suppose out of a population of 400 people, 50 have received at least one speeding ticket in the last year. If one person out of this population is selected at random, what is the probability that person has received at least one speeding ticket in the last year?

0.125

Find the value of (alpha) that corresponds to a level of confidence of 82%

0.18

Use the one-proportion z-interval procedure to find the required confidence interval. In a sample of 713 patients who underwent a certain type of surgery, 22% experienced complications. Find a 90% confidence interval for the proportion of all those undergoing this surgery who experience complications.

0.1945 to 0.2455

Suppose out of a population of 1000 people, it is believed that 800 have a genetic disorder. If one person out of the population was randomly selected, what is the probability that person will not have the genetic disorder?

0.20

Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations. The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m) are listed below.

0.2151 m

Use the following probability distribution to determine P(6 < X 8). All outcomes are mutually exclusive.

0.35

For a particular regression analysis, it is found that SST = 800.0 and SSE = 300.00. Calculate the coefficient of determination.

0.625

From a given population, it is known that 68% are female, 20% are smokers, and 16% are females who smoke. What is the probability that a randomly selected person from this population will be female or a smoker?

0.72

Summary statistics are given for independent simple random samples from two populations. Use the pooled t-interval procedure to obtain the specified confidence interval. 1 = 71.8, s1 = 3.1, n1 = 11, 2 = 67.0, s2 = 3.2, n2 = 9 Determine a 99% confidence interval.

0.73 to 8.87

A one-sample z-test for a population mean is to be performed. The value obtained for the test statistic is given. The nature of the test ( right-tailed, left-tailed or two-tailed) is also specified. Determine the p-value

0.8650

Find the requested value. A researcher wishes to estimate the mean resting heart rate for long-distance runners. A random sample of runners yields the following heart rates, in beats per minute. Use the data to obtain a point estimate of the mean resting heart rate for all long distance runners.

67.7 b/m

A researcher wishes to estimate the mean resting heart rate for long-distance runners. A random sample of runners yields the following heart rates, in beats per minute. Use the data to obtain a point estimate of the mean resting heart rate for all long distance runners.

67.7 beats per minute

According to an article, the average age of a self-employed individual is 46.6 years with a standard deviation of 10.8 years. For a sample of size 100, what is the standard deviation of the sample mean, xbar (i.e., what is the standard error for a sample of size 100)?

1.08

The mean annual salary for all public classroom teachers is assumed to be $49,000. The standard deviation of annual salary for all public classroom teachers is assumed to be $9,200. A random sample of 300 public classroom teachers is selected from which it is found an average salary of $45,000 with a standard deviation of $10,000. In this given scenario, which value is the sample standard deviation, s?

10,000

A random variable X follows a normal distribution with a mean of 10 and standard deviation of 3. A standardized value of X was found to be Z = 2.5. The value of X is then

17.5

Scores on a certain test are normally distributed with a variance of 14. A researcher wishes to estimate the mean score achieved by all adults on the test. Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more than 2 units.

20

I want to construct a 95% confidence interval on a population mean with a margin of error of no more than 3 units. If the population standard deviation is known to be 7, what sample size would be needed for this problem?

21

An office manager has implemented an incentive plan that she thinks will reduce the mean time to handle a customer complaint. The mean time for handling a complaint was 35 minutes prior to implementing the incentive plan. It was also assumed that the standard deviation of the time to handle a complete is 4 minutes. After the plan was in place for several months, a random sample of 5 customers who had complaints revealed a mean time of 28 minutes. Which of the following 95% confidence interval formulas (with the values plugged into the formula, but not completely worked out) is the correct one if we want to construct a 95% two-sided confidence interval on the true mean time to handle a customer complaint. Assume time to handle a complaint is normally distributed.

28 - 1.96(1.789) < μ < 28 + 1.96(1.789)

Apply the nonpooled t-interval procedure to obtain the required confidence interval. You may assume that the assumptions for using the procedure are satisfied. A paint manufacturer wished to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Determine a 98% confidence interval for the difference, between the mean drying time for type A and the mean drying time for type B.

4.18 to 15.42 hours

A sample of 35 people were randomly selected from among the workers in a shoe factory. The time taken for each person to polish a finished shoe was measured. The sample mean was 4.7 minutes. Assume that Construct a 90% confidence interval for the true mean time, μ, to polish a shoe. (SD=.41)

4.59 to 4.81 minutes

The mean annual salary for all public classroom teachers is assumed to be $49,000. The standard deviation of annual salary for all public classroom teachers is assumed to be $9,200. A random sample of 300 public classroom teachers is selected from which it is found an average salary of $45,000 with a standard deviation of $10,000. In this given scenario, which value is the sample mean, x-bar?

45,000

You are given some information about a sample of data. It is known that the sample variance for this set of data is 10. You are also told that the sum of the squared deviations from the sample mean is 510 (see below). What is the size of this sample?

52

Find the required sample size without making a guess for the observed value of . A manufacturer wishes to estimate the proportion of washing machines leaving the factory that are defective. Obtain a sample size that will ensure a margin of error of at most 0.014 for a 97% confidence interval.

6007

Weights of women in one age group are normally distributed with a standard deviation σ of 18 lb. A researcher wishes to estimate the mean weight of all women in this age group. Find how large a sample must be drawn in order to be 90 percent confident that the sample mean will not differ from the population mean by more than 3.8 lb.

61

Use the regression equation to predict the y-value corresponding to the given x-value. Round your answer to the nearest tenth. The regression equation relating dexterity scores (x) and productivity scores (y) for ten randomly selected employees of a company is . Predict the productivity score for an employee whose dexterity score is 32.

66.6

The number of successes and the sample size are given for a simple random sample from a population. Decide whether using the one-proportion z-test is appropriate. x = 3, n = 80, H0: p = 0.04, Ha: p > 0.04

N/A

A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects

67.7 to 84.7

Find the confidence interval specified. Assume that the population is normally distributed. A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects.

67.7 to 84.7

A researcher wishes to estimate the mean resting heart rate for long-distance runners. A random sample of 12 long distance runners yields the following heart rates, in beats per minute: 76, 58, 69, 78, 64, 61, 65, 78, 82, 58, 70, 63 Use the data to obtain a point estimate of the mean resting heart rate for all long distance runners.

68.5 b/m

Find the indicated probability or percentage for the normally distributed variable. The incomes of trainees at a local mill are normally distributed with a mean of $1,100 and a standard deviation $150. What percentage of trainees earn less than $900 a month?

9.18%

For samples of the specified size from the population described, find the mean and standard deviation of the sample mean . The National Weather Service keeps records of rainfall in valleys. Records indicate that in a certain valley, the annual rainfall has a mean of and a standard deviation of Suppose the rainfalls are sampled during randomly picked years and is the mean amount of rain in these years. For samples of size 25, determine the mean and standard deviation of .

93;2

Sara and Gerry took a math exam. Sara's percentile score on the exam was 40; Gerry's percentile score on the same test was 80. One of the following four statements is correct. Which one?

Gerry correctly answered more items than Sara did.

Suppose in past years the average price per square foot for warehouses in the US has been $32.28. A national real estate investor wants to determine whether that figure has changed now. The investor hires a researcher who randomly samples 16 warehouses and finds that the mean price per square foot is $31.68 with a standard deviation of $2.00. For this problem, which of the following would be an appropriate null hypothesis?

H0: μ = $32.28

A hypothesis test is to be performed. Determine the null and alternative hypotheses. The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.2 parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit.

H0: μ = 0.2 ppm Ha: μ > 0.2 ppm

The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.2 parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit.

H0: μ = 0.2 ppm Ha: μ > 0.2 ppm

In the past, the mean running time for a certain type of flashlight battery has been 8.7 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result.

H0:μ=8.7 and Ha: μ ≠ 8.7

The recommended dietary allowance (RDA) of vitamin C for women is 75 milligrams per day. A hypothesis test is to be performed to decide whether adult women are, on average, getting less than the RDA of 75 milligrams per day.

Left-tailed

Determine the null and alternative hypotheses for the proposed hypothesis test. A researcher wants to use a paired sample to determine whether the mean number of hours spent exercising per week for married men differs from the mean number of hours spent exercising per week for married women.

Let μ1 denote the mean number of hours spent exercising per week for married men and let μ2 denote the mean number of hours spent exercising per week for married women. The null and alternative hypotheses are and

It is known that two events, A, B, are mutually exclusive. Which of the following is true?

P(A and B) = 0

The significance level and P-value of a hypothesis test are given. Decide whether the null hypothesis should be rejected.

Reject the null hypothesis.

The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.9 parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit.

Right-tailed

Suppose a study is being conducted involving statistics about naturalized persons in the U.S. Suppose a naturalized person is chosen at random. Let A = event the person is younger than 20 years old. What is the complement of this event?

The chosen person is 20 years old or older.

A recent article in an educational research journal reports a correlation of +.8 between math achievement and overall math aptitude for a large sample of students. It also reports a correlation of of -.8 between math achievement and a math anxiety test for the same group of students. Only students with scores on all three measures were included in the study. Which of the following interpretations is the most correct?

The correlation of +.8 is just as strong as the correlation of -.8

The average on a exam is 72 with a standard deviation of 6. A student scores a 78 on the exam. Which of the following is correct?

The student's score is 1 standard deviation above the average.

Which of these statements is true? (There is only 1 correct answer)

There is a strong linear relationship between gender and height because we found a correlation of .85.

Suppose I construct a 95% confidence interval on a population mean, then I construct a 99% confidence interval on the same population mean. Everything else is held constant: sample mean, sample size, standard deviation. The 99% confidence interval will always be wider than the 95% confidence interval for the same set of data.

True

The P-value for a hypothesis test is given. Determine whether the strength of the evidence against the null hypothesis is weak/none, moderate, strong, or very strong

Very strong

A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples were obtained of 16 people aged who do not exercise regularly and 12 people aged who do exercise regularly. The resting pulse rate (in beats per minute) of each person was recorded. The summary statistics were as follows. The researcher used a pooled t-interval procedure to obtain a 90% confidence interval for the difference between the mean pulse rate of people who do not exercise regularly and the mean pulse rate of people who exercise regularly. The 90% confidence interval was found to be . Interpret this confidence interval.

We can be 90% confident that the difference between the mean pulse rate of people who do not exercise regularly and the mean pulse rate of people who exercise regularly is somewhere between .

The P-value for a one-mean t-test is estimated using a t-table as 0.025 < P < 0.05. Based on this information, for what significance levels can the null hypothesis be rejected?

We can reject H0 at any significance level 0.05 or larger.

The P-value for a one-mean t-test is estimated using a t-table as 0.05 < P < 0.10. Based on this information, for what sigificance levels can the null hypothesis be rejected?

We can reject H0 at any significance level 0.10 or larger.

True or false, the standard deviation of a normally distributed variable can be any real number.

false

Provide an appropriate response. Traditionally in hypothesis testing the null hypothesis represents the "status quo" which will be overturned only if there is evidence against it. Which of the statements below might represent a null hypothesis?

has no effect

Provide an appropriate response. What generally happens to the sampling error as the sample size is increased?

it gets smaller

An experimenter wants to conduct a hypothesis test on a claim that there was no difference between two population means. That is, H0: μ1 - μ2 = 0. The experimenter randomly selected 10 items from the first population and 10 items from the second population. The population variances are assumed to be known. Specifically, the variance of the first population is 25 and the variance of the second population is 36. If you were to conduct the test for the experimenter, which case from Chapter 10 would this problem fall under or represent?

case I

For a particular hypothesis test it is known that α = 0.10, and the p-value was found to be 0.15. Given this information, you would reject the null hypothesis being tested.

false

The recommended dietary allowance (RDA) of vitamin C for women is 75 milligrams per day. A hypothesis test is to be performed to decide whether adult women are, on average, getting less than the RDA of 75 milligrams per day. Which of the following hypothesis tests is the most appropriate for this situation?

ledt-tailed

A political pollster reports that her candidate has a 5% lead in the polls. This is an example of

observational study

We find that the correlation between educational level attained and yearly income is +0.72. This finding means that

people with lower educational levels tend to have lower incomes.

The name of a manufacturer of CD players is a

qualitative variable

The significance level and P-value of a hypothesis test are given. Decide whether the null hypothesis should be rejected. α = 0.05, P-value = 0.016

reject

Classify the hypothesis test as two-tailed, left-tailed, or right-tailed. A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct.

right-tailed

A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 243 milligrams with a standard deviation of 16.2 milligrams. We want to construct a 95% confidence interval for the true mean cholesterol content of all such eggs, which distribution is most appropriate to use to construct this interval?

t

You are going to construct a 99% confidence interval on a population mean. The size of the sample taken was n = 20 and it was taken from a normal population. What is the correct value of t to use in the confidence interval formula?

t = 2.861

The time to repair an electronic device is a normally distributed random variable measured in hours. For 16 such devices, the average repair time was found to be 240 hours with a standard deviation of 4 hours. A 95% confidence interval is to be constructed on the true average time to repair all electronic devices of this type. Which distribution are you going to use when constructing this confidence interval?

t-distribution

Classify the hypothesis test as two-tailed, left-tailed, or right-tailed. In the past, the mean running time for a certain type of flashlight battery has been 8.8 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result.

two-tailed

Suppose you earned a score of 17 on a quiz. For which of the following conditions would your score indicate the best performance in relation to the rest of the class?

μ = 15 and σ =2.1