Question 1

The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers. It wishes to estimate this difference using a 95 percent confidence level. Assume that the variances are equal and the populations normally distributed. The following data represent independent samples from each population:  Based on these data, the company can conclude that there is a statistical difference between men and women with regard to mean spending at the hardware store with men tending to spend more on average than women.

Accepted Answer

True

Question 2

Box and whisker plots are often useful for determining whether two populations have distributions that might be skewed.

Accepted Answer

Box and whisker plots visually display the distribution, median, and variability of a dataset, making it easier to compare distributions and identify skewness across different populations.

Question 3

In estimating the difference between two population means, if a 95 percent confidence interval includes zero, then we can conclude that there is a 95 percent chance that the difference between the two population means is zero.

Accepted Answer

A 95 percent confidence interval including zero means that we cannot reject the null hypothesis that there is no difference between the two population means at the 95 percent confidence level. It does not imply there is a 95 percent chance that the difference is exactly zero, but rather that the observed difference could be due to random chance.

Question 4

Increasing the size of the samples in a study to estimate the difference between two population means will increase the level of confidence that a decision maker can have regarding the interval estimate.

Accepted Answer

Increasing the sample size decreases the margin of error of the confidence interval, making the interval estimate more precise, but it does not inherently increase the level of confidence, which is determined by the chosen confidence level (e.g., 90%, 95%, 99%).

Question 5

Marketing managers for a toy store located in two separate cities is interested in estimating the difference in the mean daily sales for the two cities. They want to calculate a 90 percent confidence interval and will select a sample of 10 days in each store for the study. If the marketing managers assume that the population standard deviations are known, the critical value for the confidence interval is z = 1.645.

Accepted Answer

For a 90% confidence interval with known population standard deviations, the critical value from the standard normal distribution (z-distribution) is indeed 1.645.

Question 6

In order to make the test for the difference between two population means valid, the sample size in each independent sample must be the same.

Accepted Answer

The test for the difference between two population means can still be valid even if the sample sizes are different. The assumption of equal sample sizes is not a strict requirement for such tests, although equal or similar sample sizes can increase the power of the test.

Question 7

The NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college campuses. It wants 95 percent confidence and will select a sample of 10 men and 10 women for the study. The variances are assumed equal and the populations normally distributed. The sample results are:  Based on these data, the lower limit for the difference between population means is 0.15 hours.

Accepted Answer

The answer of The NCAA is interested in estimating the...

Question 8

The NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college campuses. It wants 95 percent confidence and will select a sample of 10 men and 10 women for the study. The variances are assumed equal and the populations normally distributed. The sample results are:  Based on these sample data, the critical value for developing the confidence interval is z = 1.96.

Accepted Answer

The answer of The NCAA is interested in estimating the...

Question 9

All other things held constant, decreasing the level of confidence for a confidence interval estimate for the difference between two population means will result in a smaller margin of error.

Accepted Answer

Decreasing the level of confidence reduces the critical value (z* or t*), which in turn decreases the margin of error since the margin of error is directly proportional to the critical value.

Question 10

The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers. It wishes to estimate this difference using a 95 percent confidence level. If the sample size is n = 10 from each population, the samples are independent, and sample standard deviations are used, and the variances are assumed equal, then the critical value will be t = 2.1009.

Accepted Answer

For a two-sample t-test with equal variances and a 95% confidence level, the degrees of freedom is n1 + n2 - 2 = 18. The critical t-value for 18 degrees of freedom at a 95% confidence level (two-tailed) is approximately 2.1009.

Question 11

The NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college campuses. They want 95 percent confidence and will select a sample of 10 men and 10 women for the study. The sample results are:  Based on these data, the point estimate is .30 hours.

Accepted Answer

The answer of The NCAA is interested in estimating the...

Question 12

The t-distribution is still applicable even when there are small violations of the assumptions for the case when the variances for two populations are unknown. This is particularly true when the sample sizes are approximately equal.

Accepted Answer

The t-distribution is robust to small violations of the normality assumption, especially when sample sizes are equal or nearly equal, and is used when population variances are unknown, making it applicable in many practical situations.

Question 13

Recently the managers for a large retail department store stated that a study has revealed that female shoppers spend on average 23.5 minutes longer in the store per visit than do male shoppers. Based on this information, the managers can be confident that female shoppers, as a population, do spend longer times in the store than do males shoppers, as a population.

Accepted Answer

The statement only indicates a finding from one study and does not account for variables such as sample size, selection bias, or the possibility of outliers. Without further evidence or replication of results, it's premature to generalize this finding to the entire population of female and male shoppers.

Question 14

In estimating the difference between two population means based on small, independent samples from the two populations, two important assumptions are that the populations each be normally distributed and the populations have equal variances.

Accepted Answer

For small, independent samples, the assumption of normality ensures the sampling distribution of the difference between means approximates a normal distribution, and the assumption of equal variances (homoscedasticity) is crucial for the validity of the test statistics used in such comparisons.

Question 15

In estimating a confidence interval for the difference between two means, when the samples are independent and the standard deviations are unknown, it can be acceptable for there to be small violations of the assumptions of normality and equal variances, especially when the sample sizes are equal.

Accepted Answer

When the sample sizes are equal, the Central Limit Theorem suggests that the sampling distribution of the difference between two means will be approximately normal, even if the original populations are not perfectly normal. Additionally, equal sample sizes can mitigate the effects of unequal variances between the two groups.

Question 16

The NCAA is interested in estimating the difference in mean number of daily training hours for men and women athletes on college campuses. It wants 95 percent confidence and will select a sample of 10 men and 10 women for the study. The variances are assumed equal and the populations normally distributed. The sample results are:  Based on these sample data, the estimate for the standard deviation of the sampling distribution is found by taking the square root of the sum of the two sample variances.

Accepted Answer

The answer of The NCAA is interested in estimating the...

Question 17

When performing a hypothesis test for the difference between the means of two independent populations, where the standard deviations are known, the variances must be assumed equal.

Accepted Answer

When performing a hypothesis test for the difference between the means of two independent populations with known standard deviations, it is not necessary to assume equal variances; one can use the z-test formula that incorporates the standard deviations of both populations directly without assuming equal variances.

Question 18

The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers. It wishes to estimate this difference using a 95 percent confidence level. Assume that the variances are equal and the populations normally distributed. The following data represent independent samples from each population:  Based on these data, the upper limit of the interval estimate is approximately $13.82.

Accepted Answer

The answer of The Cranston Hardware Company is interested in...

Question 19

Two samples are said to be independent if they are collected at different points in time.

Accepted Answer

Two samples are said to be independent if the selection of one sample does not influence or affect the selection of the other sample; it is not solely about when they are collected.

Question 20

To find a confidence interval for the difference between the means of independent samples, when the variances are unknown but assumed equal, the sample sizes of the two groups must be the same.

Accepted Answer

The sample sizes of the two groups do not need to be the same to find a confidence interval for the difference between the means of independent samples when the variances are unknown but assumed equal. The formula for the confidence interval can accommodate different sample sizes.

Quiz 10: Estimation and Hypothesis Testing for Two Population Parameters

Box and whisker plots are often useful for determining whether two populations have distributions that might be skewed.

In estimating the difference between two population means, if a 95 percent confidence interval includes zero, then we can conclude that there is a 95 percent chance that the difference between the two population means is zero.

Increasing the size of the samples in a study to estimate the difference between two population means will increase the level of confidence that a decision maker can have regarding the interval estimate.

In order to make the test for the difference between two population means valid, the sample size in each independent sample must be the same.

All other things held constant, decreasing the level of confidence for a confidence interval estimate for the difference between two population means will result in a smaller margin of error.

The t-distribution is still applicable even when there are small violations of the assumptions for the case when the variances for two populations are unknown. This is particularly true when the sample sizes are approximately equal.

In estimating the difference between two population means based on small, independent samples from the two populations, two important assumptions are that the populations each be normally distributed and the populations have equal variances.

In estimating a confidence interval for the difference between two means, when the samples are independent and the standard deviations are unknown, it can be acceptable for there to be small violations of the assumptions of normality and equal variances, especially when the sample sizes are equal.

When performing a hypothesis test for the difference between the means of two independent populations, where the standard deviations are known, the variances must be assumed equal.

Two samples are said to be independent if they are collected at different points in time.

To find a confidence interval for the difference between the means of independent samples, when the variances are unknown but assumed equal, the sample sizes of the two groups must be the same.