Question 1

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

Paired samples involve testing the same group of individuals or items twice, whereas independent samples involve testing two different groups. By using paired samples, any individual differences or external factors that could affect the results are controlled for, making it easier to accurately determine whether or not the two groups truly differ.

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.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 ρ = .1050.

Accepted Answer

The question only states a fact about the pooled estimator for the overall proportion, which is given as ρ = 0.1050. There is no additional information provided that would allow for a determination of whether this estimator indicates a significant difference between the two divisions or not.

Question 3

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 4

The Sergio Lumber Company manufacturers 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.

Accepted Answer

Since the question does not provide any hypothesis testing or the sample size, it cannot be determined whether the critical t-value is actually 1.7459 or not. Therefore, option A is true based on the information provided in the question.

Question 5

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

The point estimate for the difference between the means of two paired samples is indeed the mean value of the paired differences. This is because when two samples are paired, each observation in one sample is related to a corresponding observation in the other sample. The paired differences between these observations capture the effect of the characteristic being measured, while accounting for individual differences between the paired observations. Thus, the mean of the paired differences is a natural point estimate for the true difference between the means of the two populations.

Question 6

The Sergio Lumber Company manufacturers 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  .

Accepted Answer

The statement does not give the null and alternative hypotheses to be tested.

Question 7

When performing a hypothesis test for the difference in 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 the individual standard deviations, not the pooled standard deviation. The pooled standard deviation is used when the standard deviations are unknown and assumed to be equal.

Question 8

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. If the point estimate does not fall within the confidence interval, it simply means that the sample difference is not a good predictor of the true population difference. It does not necessarily mean that the two populations have different means.

Question 9

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:

Accepted Answer

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

Question 10

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

To determine whether there is a significant difference between the proportions of accounts receivables with errors in Division 1 and Division 2, the appropriate statistical test is a two-sample z-test for proportions. Using a significance level of 0.05 and a two-tailed test, the critical value from the standard normal table is ±1.96. However, since the question is asking about a one-tailed test (whether the proportion in Division 1 exceeds that in Division 2), the critical value is z = 1.645. Therefore, the statement is true.

Question 11

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 correct formula for finding the pooled standard deviation in a two-sample t-test.

Question 12

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-group hypothesis test with unknown standard deviation.

Accepted Answer

This statement is true. After finding the difference for each paired observation, the testing of whether the mean difference is equal to 0 is equivalent to performing a one-sample hypothesis test with an unknown population standard deviation, which is the same as what is done in a one-group hypothesis test.

Question 13

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

Since the test statistic is not significant at the 0.05 level, we fail to reject the null hypothesis that there is no difference in the mean scores of the two tests. Therefore, it is true that there is no difference in the mean scores that would be received for the two tests.

Question 14

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 15

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 question statement provides a hypothesized test statistic and mentions the assumption of normality and equal variances. The test statistic is negative, indicating that the sample mean for joint accounts is lower than that for single accounts. Without further information on the significance level or the degrees of freedom, it is not possible to reach a conclusion about the null hypothesis. However, the statement is true that the test statistic is approximately -1.49.

Question 16

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 unequal, the pooled variance estimate used in the standard t-test is biased. Therefore, an adjustment known as the Welch's t-test should be used, which provides a modified t-test statistic and degrees of freedom that account for unequal variances.

Question 17

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

When the variances are assumed equal and the population normally distributed, the pooled standard deviation can be calculated by combining the sample standard deviations and sample sizes of both populations. So, it is possible to obtain a value for the pooled standard deviation, making statement A true.

Question 18

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

These are the assumptions for a two-sample t-test for equal variances. If the variances are not equal, then the Welch's t-test should be used.

Question 19

The Sergio Lumber Company manufacturers 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 test should be a one-tailed test because it is testing if pine veneer is less moist on average than fir veneer, indicating a directional hypothesis.

Question 20

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. The t-distribution is used when the sample size is small or when the population standard deviation is unknown and must be estimated from the sample.

Quiz 10: Estimation and Hypothesis Testing for Two Population Parameters