Question 1

If you are interested in estimating the difference between the means of two samples that have been paired,the point estimate for this difference is the mean value of the paired differences.

Accepted Answer

This statement is true. When two samples have been paired, the point estimate for the difference between their means is the mean value of the paired differences.

Question 2

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.The null and alternative hypotheses that will be tested are: H₀ : μ₁ ≥ μ₂ H_a : μ₁ < μ₂

Accepted Answer

The null hypothesis should state that there is no difference or that Division 1's proportion is less than or equal to Division 2's, while the alternative hypothesis should state that Division 1's proportion exceeds Division 2's.

Question 3

When performing a hypothesis test for the difference between the means of two independent populations where the standard deviations are known,it is necessary to use the pooled standard deviation in calculating the test statistic.

Accepted Answer

When the standard deviations of two independent populations are known, the test statistic is calculated using those known standard deviations directly, rather than pooling them. Pooling is used when the population standard deviations are unknown and assumed to be equal, and sample standard deviations are used as estimates.

Question 4

There is interest at the American Savings and Loan as to whether there is a difference between average daily balances in checking accounts that are joint accounts (two or more members per account)versus single accounts (one member per account).To test this,a random sample of checking accounts was selected with the following results:
  Based upon these data,the critical value from the t-distribution for testing the difference between the two population means using a significance level of 0.05 is t = 1.6772.

Accepted Answer

The answer of There is interest at the American Savings...

Question 5

The t-distribution can be used to test hypotheses about the difference between two population means given the following two assumptions:
- each population is normally distributed,and
- the two populations have equal variances.

Accepted Answer

The two assumptions stated in the statement are correct for using the t-distribution to test hypotheses about the difference between two population means.

Question 6

In comparing two populations using paired differences,after the difference is found for each pair,the method for testing whether the mean difference is equal to 0 becomes the same as was used for a one-sample hypothesis test with unknown standard deviation.

Accepted Answer

This statement is true. The method for testing whether the mean difference is equal to 0 in paired differences becomes equivalent to a one-sample hypothesis test with unknown standard deviation.

Question 7

There is interest at the American Savings and Loan as to whether there is a difference between average daily balances in checking accounts that are joint accounts (two or more members per account)versus single accounts (one member per account).To test this,a random sample of checking accounts was selected with the following results:
  Based upon these data,assuming that the populations are normally distributed with equal variances,the test statistic for testing whether the two populations have equal means is approximately -1.49.

Accepted Answer

The statement is true based on the given information. The test statistic for testing whether the two populations have equal means is approximately -1.49.

Question 8

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 critical value from the standard normal table is z = 1.645.

Accepted Answer

The critical value from the standard normal table at a significance level of 0.05 is indeed 1.645.

Question 9

Two placement exams are available that students can take to determine which math class they should begin with in their freshman year.It is believed that there is no difference in the mean scores that would be received for the two tests.To test this using a 0.05 level of significance,a randomly selected group of students took both tests and had their scores recorded.The following data were obtained:
  Based on these data,the test statistic is approximately t = -1.892.

Accepted Answer

To test if there is a difference in mean scores, we use a paired t-test. Using the given data, we can calculate the difference in scores for each student and find the sample mean and standard deviation of those differences. With those values, we can calculate the t-statistic. In this case, the calculated t-statistic is -1.892. By comparing this value to the t-distribution with n-1 degrees of freedom (where n is the number of pairs), and a significance level of 0.05, we find that the p-value is greater than 0.05. Therefore, we fail to reject the null hypothesis that there is no difference in mean scores between the two tests. Therefore, the statement is true.

Question 10

To find the pooled standard deviation involves taking a weighted average of the two sample variances,then finding its square root.

Accepted Answer

This is the formula for calculating the pooled standard deviation when combining two samples with different variances.

Question 11

The test statistic that is used when testing hypotheses about the difference between two population proportions is the t-value from the t-distribution.

Accepted Answer

The test statistic used when testing hypotheses about the difference between two population proportions is the z-value from the standard normal distribution.

Question 12

The Sergio Lumber Company manufactures plywood.One step in the process is the one where the veneer is dried by passing through a huge dryer (similar to an oven)where much of the moisture in the veneer is extracted.At the end of this step,samples of veneer are tested for moisture content.It is believed that pine veneer will be less moist on average than will fir veneer.The following data were reported recently where the values represent the percent of moisture in the wood: The null and alternative hypotheses to be tested are H₀ : μ_p ≥ μ_f H_a : μ_p < μ_f

Accepted Answer

The answer of The Sergio Lumber Company manufactures plywood.One step...

Question 13

The Sergio Lumber Company manufactures plywood.One step in the process is the one where the veneer is dried by passing through a huge dryer (similar to an oven)where much of the moisture in the veneer is extracted.At the end of this step,samples of veneer are tested for moisture content.It is believed that pine veneer will be less moist on average than will fir veneer.The following data were reported recently where the values represent the percent moisture in the wood:
  Based on these data,the critical t value from the t-distribution will be 1.7459 if the significance level is set at 0.05 and variances are presumed equal.

Accepted Answer

The answer of The Sergio Lumber Company manufactures plywood.One step...

Question 14

When conducting a hypothesis test to determine whether or not two groups differ,using paired samples rather than independent samples has the advantage of controlling for sources of variation that might distort the conclusions of the study.

Accepted Answer

When using paired samples, each subject serves as its own control, which reduces the potential for confounding variables to influence the results. Additionally, paired samples generally provide more power and precision than independent samples, which can increase the accuracy of the hypothesis test.

Question 15

The Sergio Lumber Company manufactures plywood.One step in the process is the one where the veneer is dried by passing through a huge dryer (similar to an oven)where much of the moisture in the veneer is extracted.At the end of this step,samples of veneer are tested for moisture content.It is believed that pine veneer will be less moist on average than will fir veneer.The hypothesis test that will be conducted using an alpha = 0.05 level will be a two-tailed test.

Accepted Answer

The hypothesis suggests a specific direction (pine veneer will be less moist than fir veneer), which indicates a one-tailed test is more appropriate for testing if one mean is less than the other, not just different.

Question 16

To test whether Model A and Model B cars have the same MPG,the first step is to select two independent random samples of drivers and assign one of them to drive Model A and the other Model B.

Accepted Answer

The answer of To test whether Model A and Model...

Question 17

If the sample data lead us to suspect that the variances of the two populations are not equal,the t-test statistic and the degrees of freedom must be adjusted accordingly.

Accepted Answer

When the variances of the two populations are not equal, the t-test statistic and degrees of freedom must be adjusted using a modified formula, known as a separate variance t-test.

Question 18

If the point estimate in a paired difference estimation example does not fall in the resulting confidence interval,the decision maker can conclude that the two populations likely have different means.

Accepted Answer

This statement is incorrect. The decision maker cannot conclude that the two populations have different means solely based on the point estimate falling outside the confidence interval. The confidence interval only provides a range of values where the true population mean difference is likely to fall with a certain level of confidence. It is possible for the true population mean difference to be different from the point estimate and still fall within the confidence interval. To make conclusions about the difference in population means, additional information and analysis may be necessary.

Question 19

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 pooled estimator for the overall proportion is  = .1050.

Accepted Answer

The statement is true as the pooled estimator for the overall proportion provided in the question (0.1050) suggests that there is a common proportion of accounts with errors in both divisions.

Question 20

In order to test the difference in populations means,samples were collected for two independent populations where the variances are assumed equal and the population normally distributed.The following data resulted:
  The value of the pooled standard deviation is 15.66.

Accepted Answer

The statement mentions that the variances are assumed equal and the populations are normally distributed. In such a scenario, the pooled standard deviation can be calculated as the square root of the weighted average of the sample variances. Hence, the given value of the pooled standard deviation (15.66) could be valid, making Option A the correct answer.

Quiz 10: Estimation and Hypothesis Testing for Two Population Parameters