Question 1

When estimating a confidence interval for the difference between 2 means using the method where sample variances are pooled, which of the following assumptions is not needed?
A) The populations are normally distributed.
B) The populations have equal variances.
C) The samples are independent.
D) The sample sizes are equal.

Accepted Answer

The assumption that the sample sizes must be equal is not needed when estimating a confidence interval for the difference between two means using the pooled variance method. The method requires the assumption of equal variances (B) but can accommodate unequal sample sizes.

Question 2

A recent study posed the question about whether Japanese managers are more motivated than American managers. A randomly selected sample of each was administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.  Judging from the way the data were collected, which test would likely be most appropriate?
A) Related samples t-test for mean difference
B) Pooled-variance t-test for the difference in means
C) Independent samples Z-test for the difference in means
D) Related samples Z-test for mean difference

Accepted Answer

The answer of A recent study posed the question about...

Question 3

A direct retailer that sells clothing on the Internet has two distribution centers and wants to determine if there is a difference between the proportion of customer order shipments that contain errors (wrong color, wrong size, etc.). It takes a sample of orders from each distribution center and obtain the following results:  Based on these data it can proceed with assuming the normal distribution for each of the proportion sampling distributions.

Accepted Answer

The answer of A direct retailer that sells clothing on...

Question 4

A major manufacturer of home electronics is interested in determining whether customers have a preference between two new speaker designs for their home entertainment centers. To test this, the design department manager has selected a random sample of customers and shown them the first design. A second sample of customers is shown design 2. The manager then asks each customer whether they prefer the new design they were shown over the one they currently own. The following results were observed:  Based on these data and a significance level equal to 0.05, the test statistic is approximately -4.22 and thus the null hypothesis should be rejected.

Accepted Answer

The answer of A major manufacturer of home electronics is...

Question 5

A direct retailer that sells clothing on the Internet has two distribution centers and wants to determine if there is a difference between the proportion of customer order shipments that contain errors (wrong color, wrong size, etc.). It calculates a 95 percent confidence interval on the difference in the sample proportions to be -0.012 to 0.037. Based on this, it can conclude that the distribution centers differ significantly for the proportion of orders with errors.

Accepted Answer

The confidence interval includes 0, which means there is no statistically significant difference between the proportions of order errors at the two distribution centers.

Question 6

A company in Maryland has developed a device that can be attached to car engines, which it believes will increase the miles per gallon that cars will get. The owners are interested in estimating the difference between mean mpg for cars using the device versus those that are not using the device. The following data represent the mpg for independent random samples of cars from each population. The variances are assumed equal and the populations normally distributed.  Given this data, what is the critical value if the owners wish to have a 90 percent confidence interval estimate?
A) t = 2.015
B) t = 1.7823
C) z = 1.645
D) z = 1.96

Accepted Answer

The answer of A company in Maryland has developed a...

Question 7

A commuter has two different routes available to drive to work. She wants to test whether route A is faster than route B. The best hypotheses are: 
A)

B)

C)

D)

Accepted Answer

The answer of A commuter has two different routes available...

Question 8

A major retail clothing store is interested in estimating the difference in mean monthly purchases by customers who use the store's in-house credit card versus using a Visa, Mastercard, or one of the other major credit cards. To do this, it has randomly selected a sample of customers who have made one or more purchases with each of the types of credit cards. The following represents the results of the sampling:  Given this information, which of the following statements is true?
A) If either of the sample sizes is increased, the resulting confidence interval will have a smaller margin of error.
B) If the confidence level were changed from 95 percent to 90 percent, the margin of error in the estimate would be reduced.
C) Neither A nor B are true.
D) Both A and B are true.

Accepted Answer

The answer of A major retail clothing store is interested...

Question 9

If the population variances are assumed to be known in an application where a manager wishes to estimate the difference between two population means, the 90 percent confidence interval estimate can be developed using which of the following critical values?
A) z = 1.645
B) z = 1.96
C) t value that depends on the sample sizes from the two populations
D) z = 2.575

Accepted Answer

The answer of If the population variances are assumed to...

Question 10

A company in Maryland has developed a device that can be attached to car engines, which it believes will increase the miles per gallon that cars will get. The owners are interested in estimating the difference between mean mpg for cars using the device versus those that are not using the device. The following data represent the mpg for random independent samples of cars from each population. The variances are assumed equal and the populations normally distributed.  Given this data, what is the upper limit for a 95 percent confidence interval estimate for the difference in mean mpg?
A) Approximately 3.88 mpg
B) About 5.44 mpg
C) Just under 25.0
D) None of the above

Accepted Answer

The answer of A company in Maryland has developed a...

Question 11

A major retail clothing store is interested in estimating the difference in mean monthly purchases by customers who use the store's in-house credit card versus using a Visa, Mastercard, or one of the other major credit cards. To do this, it has randomly selected a sample of customers who have made one or more purchases with each of the types of credit cards. The following represents the results of the sampling:  Based on these sample data, what is the lower limit for the 95 percent confidence interval estimate for the difference between population means?
A) About $5.28
B) Approximately $4.85
C) Approximately $2.54
D) Approximately $3.41

Accepted Answer

The answer of A major retail clothing store is interested...

Question 12

The management of a department store is interested to estimate the difference in the amount of money spent by female and male shoppers. You are given the following information.  A 95 percent confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is:
A) 49 to 64
B) 11.68 to 18.32
C) 125 to 140
D) 8 to 10

Accepted Answer

The answer of The management of a department store is...

Question 13

A major manufacturer of home electronics is interested in determining whether customers have a preference between two new speaker designs for their home entertainment centers. To test this, the design department manager has selected a random sample of customers and shown them the first design. A second sample of customers is shown design 2. The manager then asks each customer whether they prefer the new design they were shown over the one they currently own. The following results were observed:  Based on these data and a significance level equal to 0.05, the appropriate null and alternative hypotheses are: H0 : 1 ≥ 2 Ha : 1 < 2

Accepted Answer

The answer of A major manufacturer of home electronics is...

Question 14

An Internet service provider is interested in estimating the proportion of homes in a particular community that have computers but do not already have Internet access. To do this, the company has selected a random sample of n = 200 homes and made calls. A total of 188 homes responded to the survey question with 38 saying that they had a computer with no Internet access. The 95 percent confidence interval estimate for the true population proportion is approximately 0.1447 - 0.2595.

Accepted Answer

The confidence interval for a proportion is calculated using the formula $p \pm Z \sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion, $Z$ is the Z-score corresponding to the desired confidence level (for 95% confidence, $Z \approx 1.96$), and $n$ is the sample size. Given $n = 200$ and $38$ out of $188$ responses indicating they have a computer but no Internet, the sample proportion $p = \frac{38}{200} = 0.19$. Plugging these values into the formula yields a confidence interval that approximately matches the given range of $0.1447 - 0.2595$, assuming the calculation accounts for the finite population correction factor or other adjustments for the response rate.

Question 15

Given the following information, calculate the degrees of freedom that should be used in the pooled- standard deviation t-test.
A) df = 41
B) df = 39
C) df = 16
D) df = 25

Accepted Answer

The degrees of freedom (df) for a pooled-standard deviation t-test can be calculated using the formula df = n1 + n2 - 2, where n1 and n2 are the sample sizes of the two groups being compared. Without the specific sample sizes given, we cannot calculate the exact degrees of freedom. However, choice B (df = 39) suggests a scenario where the total sample size minus 2 (for the two groups) is considered, which aligns with the formula for calculating degrees of freedom in a t-test scenario. This is a common outcome when dealing with two groups of data, indicating that the total sample size across both groups is 41, leading to 39 degrees of freedom after adjusting for the two groups.

Question 16

A recent study posed the question about whether Japanese managers are more motivated than American managers. A randomly selected sample of each was administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.  Which of the following is the correct the null and alternative hypotheses to determine if the average SSATL score of Japanese managers differs from the average SSATL score of American managers? 
A) 
B) 
C) 
D)

Accepted Answer

The answer of A recent study posed the question about...

Question 17

If we are testing for the difference between the means of two independent populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to:
A) 39
B) 38
C) 19
D) 18

Accepted Answer

The degrees of freedom for the difference between the means of two independent samples is calculated as n1 + n2 - 2, which is 20 + 20 - 2 = 38.

Question 18

A major retail clothing store is interested in estimating the difference in mean monthly purchases by customers who use the store's in-house credit card versus using a Visa, Mastercard, or one of the other major credit cards. To do this, it has randomly selected a sample of customers who have made one or more purchases with each of the types of credit cards. The following represents the results of the sampling:  Suppose that the managers wished to test whether there is a statistical difference in the mean monthly purchases by customers using the two types of credit cards, using a significance level of .05, what is the value of the test statistic assuming the standard deviations are known?
A) t = 3.49
B) z = 11.91
C) z = 2.86
D) z = 3.49

Accepted Answer

The answer of A major retail clothing store is interested...

Question 19

If a manager wishes to develop a confidence interval estimate for estimating the difference between two population means, an increase in confidence level will result in:
A) a decrease in the size of the critical value.
B) a wider confidence interval.
C) a need for an increased sample size.
D) all of the above.

Accepted Answer

Increasing the confidence level results in a wider confidence interval because a higher confidence level means capturing a broader range of values to ensure the true difference between the two population means falls within the interval. This does not necessarily decrease the size of the critical value or require an increased sample size directly, although a wider interval might suggest a desire for more precision, which could lead to considering a larger sample.

Question 20

An accounting firm has been hired by a large computer company to determine whether the proportion of accounts receivables with errors in one division (Division 1) exceeds that of the second division (Division 2). The managers believe that such a difference may exist because of the lax standards employed by the first division. To conduct the test, the accounting firm has selected random samples of accounts from each division with the following results.  Based on this information and using a significance level equal to 0.05, the test statistic for the hypothesis test is approximately 1.153 and, therefore, the null hypothesis is not rejected.

Accepted Answer

The answer of An accounting firm has been hired by...

Quiz 10: Estimation and Hypothesis Testing for Two Population Parameters

When estimating a confidence interval for the difference between 2 means using the method where sample variances are pooled, which of the following assumptions is not needed?

A commuter has two different routes available to drive to work. She wants to test whether route A is faster than route B. The best hypotheses are:

If the population variances are assumed to be known in an application where a manager wishes to estimate the difference between two population means, the 90 percent confidence interval estimate can be developed using which of the following critical values?

Given the following information, calculate the degrees of freedom that should be used in the pooled- standard deviation t-test.

If we are testing for the difference between the means of two independent populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to:

If a manager wishes to develop a confidence interval estimate for estimating the difference between two population means, an increase in confidence level will result in: