Econ 426 exam 2

According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected. the mean of all the sample proportions of customers who will make a purchase after visiting the website is _______.

0.15

In testing for the differences between the means of two independent populations, you assume that the 2 populations each follow a _______ distribution.

normal

John has two jobs. For daytime work at a jewelry store, he is paid $15,000 per month, plus a commission. His monthly commission is normally distributed with a mean $10,000 and a standard deviation $2000. At night he works occasionally as a waiter, for which his monthly income is normally distributed with a mean $1,000 and a standard deviation of $300. John's income levels from these two sources are independent of each other. John's commission from the jewelry store will be between what two values symmetrically distributed around the population mean 80% of the time? Answers: $6710.29 and $12563.10 $6710.29 and $13289.71 $7436.90 and $12563.10 $7436.90 and $13289.7

$7436.90 and $12563.10

For some value of Z, the value of the cumulative standardized normal distribution is 0.2090. What is the value of Z?

- 0.81

A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot". A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e. if there is evidence that the population proportion of "like the ads a lot" for the company's ads is less than0.22) at a 0.01 level of significance. Referring to Scenario 9-1, what critical value should the company officials use to determine the rejection region?

-2.3263

The distribution of the number of loaves of bread sold per week by a large bakery over the past 5 years has a mean of 7,750 and a standard deviation of 145 loaves. Suppose a random sample of n = 40 weeks has been selected. What is the approximate probability that the mean number of loaves sold in the sampled weeks exceeds 7,895 loaves?

0

Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. What is the probability that the time interval between two consecutive defective light bulbs will be at least 90 minutes? Answers: 0.1111 0.4444 0.2778 0.0

0.0

According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected. what is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the website?

0.0015

A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot". A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e. if there is evidence that the population proportion of "like the ads a lot" for the company's ads is less than0.22) at a 0.01 level of significance. Referring to Scenario 9-1, the largest level of significance at which the null hypothesis will not be rejected is ______.

0.0135

At a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be below 0.95 centimeters?

0.0418

According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected. he standard deviation of all the sample proportions of customers who will make a purchase after visiting the website is ________.

0.05050

John has two jobs. For daytime work at a jewelry store, he is paid $15,000 per month, plus a commission. His monthly commission is normally distributed with a mean of $10,000 and a standard deviation of $2000. At night he works occasionally as a waiter, for which his monthly income is normally distributed with a mean $1,000 and a standard deviation of $300. John's income levels from these two sources are independent of each other. For a given month, what is the probability that John's commission from the jewelry store is between $5,000 and $7,000? Answers: 0.5987 0.0606 0.3829 0.4498

0.0606

A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounces. Referring to the above scenario, match the following with correct the proportion of all jars packaged by this process that have weights that fall above 10.95 ounces.

0.0668

Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. what is the probability that the time interval between two consecutive defective light bulbs will be less than 10 minutes? Answers: 0.2778 0.1111 0.4444 0.298

0.1111

According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected. what proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the website?

0.1596

The time between arrivals of customers at a bank during the noon-to-1 P.M. hour has a uniform distribution between 0 to 120 seconds. What is the probability that the time between the arrival of two customers will be less than 20 seconds? Answers: 0.1667 0.2 0.3333 0.7083

0.1667

A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. A 99% confidence interval for the proportion of cases of recidivism would go from __________ to __________. 0.3352 to 0.4148 0.063 to 0.117 0.189 to 0.331 None of the above

0.189 to 0.331

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain between 82 and 100 grams of tea leaves?

0.2132

At a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be between 0.99 and 1.01 centimeters?

0.2736

Assume that house prices in a neighborhood are normally distributed with a standard deviation of $20,000. A random sample of 16 observations is taken. What is the probability that the sample mean differs from the population mean by more than $5,000?

0.3174

The value of the cumulative standardized normal distribution at Z is 0.6255. What is the value of Z?

0.32

The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample exceeds 36.01 oz. is __________. 0.8849 0.3446 0.9836 0.1891

0.3446

A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct. In the survey on 200 managers, 58% of the managers have caught salespeople cheating on an expense report, 50% have caught salespeople working a second job on company time, 22% have caught salespeople listing a "strip bar" as a restaurant on an expense report, and 19% have caught salespeople giving a kickback to a customer. Find a 95% confidence interval estimate of the population proportion of managers who have caught salespeople working a second job on company time. 0.5116 to 0.6484 0.4307 to 0.5693 0.1626 to 0.2774 0.1356 to 0.2444

0.4307 to 0.5693

According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected. what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the website?

0.5

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain at least 100 grams of tea leaves?

0.6554

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain less than 100 grams or more than 120 grams of tea leaves?

0.6892

A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounces. the proportion of all jars packaged by this process that have weights that fall below 10.875 ounces.

0.8944

Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2, what is the probability that X is between 47 and 54?

0.91

You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 55 and 90? Answers: 0.9105 0.4332 0.9546 0.0896

0.9105

For some value of Z, the value of the cumulative standardized normal distribution is 0.8340. What is the value of Z?

0.97

The value of the cumulative standardized normal distribution at 1.5X is 0.9332. What is the value of X?

1.00

At a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12 computer chips is taken. Above what value do 2.5% of the sample means fall?

1.06

The value of the cumulative standardized normal distribution at Z is 0.8770. What is the value of Z?

1.16

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. So, the middle 70% of all sample means will fall between what two values?

104 and 115

Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and a standard deviation of 3.0 while the second sample has a mean of 33.0 and a standard deviation of 4.0. Referring to Scenario 3, the pooled (i.e., combined) variance is _______.

12.5

Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0while the second sample has a mean of 33.0 and a standard deviation of 4.0. Referring to Scenario 3, the computed t statistic is _______.

2.50

According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected. 90% of the samples will have less than what percentage of customers who will make a purchase after visiting the website?

21.47%

A hotel chain wants to estimate the mean number of rooms rented daily in a given month. The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 240 rooms. During February, a sample of 25 days has a sample mean of 370 rooms. a 99% confidence interval for the mean number of rooms rented daily in a given month is from __________ to __________. 123.6398 to 493.64 123.6398 to 246.3602 246.36% and 493.64% 246.3602 to 493.6398

246.3602 to 493.6398

A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points. What is the needed sample size to obtain a 95% confidence interval in estimating the percentage of the targeted young adults who will purchase the new game to within±5%?

384

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. 95% of all sample means will fall between what two values?

41 and 49

Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and a standard deviation of 3.0while the second sample has a mean of 33.0 and a standard deviation of 4.0. Referring to Scenario 3, there are _______ degrees of freedom for this test.

48

The time between arrivals of customers at a bank during the noon-to-1 P.M. hour has a uniform distribution between 0 to 120 seconds. What are the mean and standard deviation of the time between arrivals? Answers: 50 and 34.6410 60 and 34.6410 30 and 5.7735 60 and 5.7735

60 and 34.6410

John has two jobs. For daytime work at a jewelry store, he is paid $15,000 per month, plus a commission. His monthly commission is normally distributed with a mean $10,000 and a standard deviation $2000. At night he works occasionally as a waiter, for which his monthly income is normally distributed with a mean $1,000 and a standard deviation of $300. John's income levels from these two sources are independent of each other. The probability is 0.95 that John's commission from the jewelry store is at least how much in a given month? Answers: $6982.22 $4598.70 $6710.29 $5987.40

6710.29

You were told that the amount of time lapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive trades will be longer than 17 seconds? Answers: 7% 13% 91% 30%

7%

According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected. 90% of the samples will have more than what percentage of customers who will make a purchase after visiting the website?

8.536%

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The mean of the sampling distribution of the sample mean is __________ minutes.

80

Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and a standard deviation of 3.0while the second sample has a mean of 33.0 and a standard deviation of 4.0. Referring to Scenario 3, the critical values for a two-tail test of the null hypothesis of no difference in the population means at the α = 0.05 level of significance are _______.

?

The value that separates a rejection region from a non-rejection region is called the _______.

Critical value

A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points. True or False: Referring to the above Scenario, the report contains all the essential components for an ethical reporting of poll results.

False

True or False: A population parameter is used to estimate a confidence interval.

False

True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.02.

False

True or False: A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test, and found out that the variances were equal. For this situation, the professor should use a t-test with related samples.

False

True or False: For a given level of significance, if the sample size is increased but the summary statistics remain the same, the probability of committing a Type I error will increase.

False

True or False: Holding the level of confidence fixed, increasing the sample size will lead to a wider confidence interval.

False

True or False: If a data set is approximately normally distributed, its normal probability plot would be S-shaped.

False

True or False: The "middle spread," that is the middle 50% of the normal distribution, is equal to one standard deviation.

False

True or False: The confidence interval obtained will always correctly estimate the population parameter.

False

You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15. What decision will you make if we test H0 : μ=16 versus H1 :μ≠ 16 at α = 0.10? Reject H0 in favor of H1. Do not reject H0 in favor of H1. Fail to reject H0 in favor of H1. Fail to reject H0 in favor of H1.

Reject H0 in favor of H1.

True or False: A researcher is curious about the effect of sleep on students' test performances. He chooses 60 students and gives each two tests: one given after two hours' sleep and one after eight hours sleep. The test the researcher should use would be a related samples test.

True

True or False: Any set of normally distributed data can be transformed to its standardized form.

True

True or False: As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.

True

True or False: The Central Limit Theorem ensures that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

True

True or False: The difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.

True

If you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample S = 0.05, the critical value of t will be a) 2.7969 b) 2.7874 c) 2.4922 d) 2.4851

a) 2.7969

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, 75.8% of the college students will take more than how many minutes when trying to find a parking spot in the library parking lot? a) 2.8 minutes b) 3.2 minutes c) 3.4 minutes d) 4.2 minutes

a) 2.8 minutes

Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width? a) Increase the sample size. b) Increase the confidence level. c) Increase the population mean. d) Increase the sample mean.

a) Increase the sample size.

Suppose a sample of n = 50 items is selected from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with μ = 6 ounces and σ = 2.5 ounces. Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected? a) The mean of the sampling distribution is 6 ounces. b) The standard deviation of the sampling distribution is 2.5 ounces. c) The shape of the sampling distribution is approximately normal. d) All of the above are correct.

a) The mean of the sampling distribution is 6 ounces.

Referring to Scenario 7, suppose α = 0.05. Which of the following represents the correct conclusion for a test on a difference in the variances? Answers: a) There is no evidence of a difference in the variances. b) There is evidence of a difference in the variances. c) There is no evidence that the variances are the same. d) There is evidence that variances are the same.

a) There is no evidence of a difference in the variances.

In testing for differences between the means of 2 related populations where the variance of the differences is unknown, the degrees of freedom are Answers: a) n - 1. b) n1 + n2 - 1. c) n1 + n2 - 2. d) n - 2.

a) n - 1.

The Y-intercept (b0) represents the a) predicted value of Y when X = 0. b) change in estimated Y per unit change in X. c) predicted value of Y. d) variation around the sample regression line.

a) predicted value of Y when X = 0.

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. before and after Student 1 530 670 Student 2 690 770 Student 3 910 1000 Student 4 700 710 Student 5 450 550 Student 6 820 870 Student 7 820 770 Student 8 630 610 Referring to the Scenario 4, at the 0.05 level of significance, the decision for this hypothesis test would be: Answers: a) reject the null hypothesis. b) do not reject the null hypothesis. c) reject the alternative hypothesis. d) It cannot be determined from the information given.

a) reject the null hypothesis.

If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic a) unbiased. b) minimum variance. c) biased. d) random.

a) unbiased.

For a given level of significance (α), if the sample size n is increased, the probability of a Type II error (β) a) will decrease. b) will increase. c) will remain the same. d) cannot be determined.

a) will decrease.

Referring to Scenario 1, what is the value of the test statistic? Selected Answer: a) -14.08 b) -11.8092 c) -1.9677 d) 96.4471

b) -11.8092

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes. a) 0.3551 b) 0.3085 c) 0.2674 d) 0.1915

b) 0.3085

The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. What is an efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress? a) 740 b) 830 c) 920 d) 1,660

b) 830

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues are the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X (read X_bar) = 52, S = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60. a) H0 : μ≤ 60 and H1 : μ > 60 b) H0: μ≥ 60 and H1 : μ < 60 c) H0 : ≥ 60 and H1 : X < 60 c) H0 : ≥ 60 and H1 : X < 60

b) H0: μ≥ 60 and H1 : μ < 60

Which of the following is not true about the Student's t distribution? a) It has more area in the tails and less in the center than does the normal distribution. b) It is used to construct confidence intervals for the population mean when the population standard deviation is known. c) It is bell-shaped and symmetrical. d) As the number of degrees of freedom increases, the t distribution approaches the normal distribution.

b) It is used to construct confidence intervals for the population mean when the population standard deviation is known.

Are Japanese managers more motivated than American managers? A randomly selected group of each was administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. American Sample Size 211 Sample Mean SSATL Score65.75 Sample Std. Dev. 11.07 Japanese Sample Size 100 Sample Mean SSATL Score 79.83 Sample Std. Dev. 6.41 Referring to Scenario 1, judging from the way the data were collected, which test would likely be most appropriate to employ? a) Paired t-test b) Pooled-variance t-test for the difference between two means c) F test for the ratio of two variances d) Z test for the difference between two proportions

b) Pooled-variance t-test for the difference between two means

The least squares method minimizes which of the following? Answers: a) SSR b) SSE c) SST d) All of the above

b) SSE

A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Suppose α = 0.05. Which of the following represents the result of the relevant hypothesis test? Answers: a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to make a decision.

b) The null hypothesis is rejected.

A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes. Gotham Xg= 35 months Xg^2= 900 Metropolis Xm= 50 months Xm^2= 1050 Referring to Scenario 2, suppose α = 0.10. Which of the following represents the result of the relevant hypothesis test? Answers: a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to make a decision.

b) The null hypothesis is rejected.

An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the mean daily revenue was $675 with a population standard deviation of $75. A sample of 30 days reveals a daily mean revenue of $625. If you were to test the null hypothesis that the daily mean revenue was $675 and decide not to reject the null hypothesis, what can you conclude? a) There is not enough evidence to conclude that the daily mean revenue was $675. b) There is not enough evidence to conclude that the daily mean revenue was not $675. c) There is enough evidence to conclude that the daily mean revenue was $675. d) There is enough evidence to conclude that the daily mean revenue was not $675.

b) There is not enough evidence to conclude that the daily mean revenue was not $675.

If an economist wishes to determine whether there is evidence that mean family income in a community exceeds $50,000 a) either a one-tail or two-tail test could be used with equivalent results. b) a one-tail test should be utilized. c) a two-tail test should be utilized. d) None of the above.

b) a one-tail test should be utilized.

If a test of hypothesis has a Type I error probability (α) of 0.01, it means that a) if the null hypothesis is true, you don't reject it 1% of the time. b) if the null hypothesis is true, you reject it 1% of the time. c) if the null hypothesis is false, you don't reject it 1% of the time. d) if the null hypothesis is false, you reject it 1% of the time.

b) if the null hypothesis is true, you reject it 1% of the time.

A university system enrolling hundreds of thousands of students is considering a change in the way students pay for their education. Currently, the students pay $400 per credit hour. The university system administrators are contemplating charging each student a set fee of $7,000 per quarter, regardless of how many credit hours each takes. To see if this proposal would be economically feasible, the administrators would like to know how many credit hours, on average, each student takes per quarter. A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter. Suppose the administration wanted to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard deviation provided a good estimate for the population standard deviation. How large a total sample would they need to take? a) n = 1,844 b) n = 2033 c) n = 2031 d) n = 2032

b) n = 2033

Sampling distributions describe the distribution of Selected Answer: a) parameters. b) statistics. c) both parameters and statistics. d) neither parameters nor statistics.

b) statistics.

The residuals represent Answers: a) the difference between the actual Y values and the mean of Y. b) the difference between the actual Y values and the predicted Y values. c) the square root of the slope. d) the predicted value of Y for the average X value.

b) the difference between the actual Y values and the predicted Y values.

The slope (b1) represents Answers: a) predicted value of Y when X = 0. b) the estimated average change in Y per unit change in X. c) the predicted value of Y. d) variation around the line of regression.

b) the estimated average change in Y per unit change in X.

Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and a standard deviation of 3.0while the second sample has a mean of 33.0 and a standard deviation of 4.0. Referring to Scenario 3, a two-tail test of the null hypothesis of no difference would _______ (be rejected/not be rejected) at the α = 0.05 level of significance.

be rejected

A 99% confidence interval estimate can be interpreted to mean that a) if all possible samples of size n are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval. b) we have 99% confidence that we have selected a sample whose interval does include the population mean. c) Both of the above. d) None of the above.

c) Both of the above.

For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a right skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. a) Distribution is right skewed with mean = 10 minutes and standard error = 0.8 minutes. b) Distribution is right skewed with mean = 10 minutes and standard error = 8 minutes. c) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes. d) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes.

c) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes.

Which of the following about the normal distribution is not true? a) Theoretically, the mean, median, and mode are the same. b) About 2/3 of the observations fall within ± 1 standard deviation from the mean. c) It is a discrete probability distribution. d) Its parameters are the mean, μ, and standard deviation, σ .

c) It is a discrete probability distribution.

A confidence interval was used to estimate the proportion of statistics students who are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60? a) No, and we are 90% sure of it. b) No. The proportion is 54.17%. c) Maybe. 0.60 is a believable value of the population proportion based on the information above. d) Yes, and we are 90% sure of it.

c) Maybe. 0.60 is a believable value of the population proportion based on the information above.

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to have a level of significance at 0.01, what rejection region should she use? a) Reject H0 if t < - 2.3263. b) Reject H0 if t < - 2.5758. c) Reject H0 if t > 2.3263. d) Reject H0 if t > 2.5758.

c) Reject H0 if t > 2.3263.

Which of the following would be an appropriate alternative hypothesis? a) The mean of a population is equal to 55. b) The mean of a sample is equal to 55. c) The mean of a population is greater than 55. d) The mean of a sample is greater than 55.

c) The mean of a population is greater than 55.

The Central Limit Theorem is important in statistics because a) for a large n, it says the population is approximately normal. b) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size. c) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. d) for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

c) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.

A ------------------ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis. a) significance level b) critical value c) test statistic d) parameter

c) test statistic

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield X_bar = 180.975 and S = 143.042. Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments. a) $180.975± $94.066 b) $180.975± $99.123 c) $180.975± $116.621 d) $180.975± $119.586

d) $180.975± $119.586

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose that the test statistic is - 2.20. Can you conclude that H0 should be rejected at the (a) α = 0.10, (b) α = 0.05, and (c) α = 0.01 level of Type I error? a) (a) yes; (b) yes; (c) yes b) (a) no; (b) no; (c) no c) (a) no; (b) no; (c) yes d) (a) yes; (b) yes; (c) no

d) (a) yes; (b) yes; (c) no

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a parking spot in the library parking lot. a) 0.0919 b) 0.2255 c) 0.4938 d) 0.7745

d) 0.7745

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X_bar = $50.50 and S = 20. Assuming the distribution of the amount spent on their first visit is normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for μ? a) Approximately normal with a mean of $50.50 b) A standard normal distribution c) A t distribution with 15 degrees of freedom d) A t distribution with 14 degrees of freedom

d) A t distribution with 14 degrees of freedom

The standard error of the mean Selected Answer: a) is never larger than the standard deviation of the population. b) decreases as the sample size increases. c) measures the variability of the mean from sample to sample. d) All of the above.

d) All of the above.

If a particular set of data is approximately normally distributed, we would find that approximately a) 2 of every 3 observations would fall between ± 1 standard deviation around the mean. b) 4 of every 5 observations would fall between ± 1.28 standard deviations around the mean. c) 19 of every 20 observations would fall between ± 2 standard deviations around the mean. d) All the above.

d) All the above.

The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, approximately how large a sample did her assistant use to determine the interval estimate? a) 2 b) 3 c) 12 d) It cannot be determined from the information given.

d) It cannot be determined from the information given.

Which of the following statements is not true about the level of significance in a hypothesis test? a) The larger the level of significance, the more likely you are to reject the null hypothesis. b) The level of significance is the maximum risk we are willing to accept in making a Type I error. c) The significance level is also called the α level. d) The significance level is another name for Type II error.

d) The significance level is another name for Type II error.

Which of the following statements about the sampling distribution of the sample mean is incorrect? a) The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n ≥ 30 ). b) The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means. c) The mean of the sampling distribution of the sample mean is equal to μ. d) The standard deviation of the sampling distribution of the sample mean is equal to σ.

d) The standard deviation of the sampling distribution of the sample mean is equal to σ.

The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a GPS navigation system if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the GPS navigation system. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30 and decided not to reject the null hypothesis, what conclusion could you reach? a) There is sufficient evidence that the proportion is 0.30. b) There is not sufficient evidence that the proportion is 0.30. c) There is sufficient evidence that the proportion is 0.30. d) There is not sufficient evidence that the proportion is not 0.30.

d) There is not sufficient evidence that the proportion is not 0.30.

It is desired to estimate the mean total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct? a) 95% of the sampled total compensation values fell between $2,181,260 and $5,836,180. b) We are 95% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to $5,836,180. c) In the population of Service industry CEOs, 95% of them will have total compensations that fall in the interval $2,181,260 to $5,836,180. d) We are 95% confident that the mean total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180.

d) We are 95% confident that the mean total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180.

For sample size 1, the sampling distribution of the mean will be normally distributed a) regardless of the shape of the population. b) only if the shape of the population is symmetrical. c) only if the population values are positive. d) only if the population is normally distributed.

d) only if the population is normally distributed.

A major home improvement store conducted its biggest brand recognition campaign in the company's history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot". A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot." The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e. if there is evidence that the population proportion of "like the ads a lot" for the company's ads is less than0.22) at a 0.01 level of significance. Referring to Scenario 9-1, the parameter the company officials is interested in is: a) the mean number of viewers who "like the ads a lot". b) the total number of viewers who "like the ads a lot". c) the mean number of company officials who "like the ads a lot". d) the proportion of viewers who "like the ads a lot".

d) the proportion of viewers who "like the ads a lot".

A Type II error is committed when a) you reject a null hypothesis that is true. b) you don't reject a null hypothesis that is true. c) you reject a null hypothesis that is false. d) you don't reject a null hypothesis that is false.

d) you don't reject a null hypothesis that is false.

The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. The accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2". True or False: Referring to Scenario 5, the null hypothesis should be rejected at the level of significance of 0.05.

false

True or False: For all two-sample tests, the sample sizes must be equal in the two groups.

false

True or False: Regression analysis is used for prediction, while correlation analysis is used to measure the strength of the association between two numerical variables.

true