Question 1

In a test for determining whether two population variances are the same or different,the larger the sample sizes from the two populations,the lower will be the chance of making a Type I statistical error.

Accepted Answer

The chance of making a Type I error, denoted by alpha (α), is determined by the significance level set for the test, not by the sample sizes. The significance level is chosen by the researcher before conducting the test and does not change with sample size.

Question 2

One of the key quality characteristics in many service environments is that the variation in service time be reasonably small.Recently,a major amusement park company initiated a new line system at one of its parks.It then wished to compare this new system with the old system in place at a comparable park in another state.At issue is whether the standard deviation in waiting time is less under the new line system than under the old line system.The following information was collected: Assuming that it wishes to conduct the test using a 0.05 level of significance,the correct null and alternative hypotheses would be: H₀ : ≠ H_a : =

Accepted Answer

The answer of One of the key quality characteristics in...

Question 3

One of the major automobile makers has developed two new engines.At question is whether the two engines have the same variability with respect to miles per gallon.To test this using a 0.10 level of significance,the following information is available:
  Based on this situation and the information provided,the null hypothesis cannot be rejected and it is possible that the two engines produce the same variation in mpg.

Accepted Answer

The answer of One of the major automobile makers has...

Question 4

A first step in testing whether two populations have the same mean value using the t-distribution is to use the chi-square distribution to test whether the populations have equal variances.

Accepted Answer

The answer of A first step in testing whether two...

Question 5

In a two-tailed hypothesis test involving two population variances,if the null hypothesis is true then the F-test statistic should be approximately equal to 1.0.

Accepted Answer

When the null hypothesis is true and the variances of two populations are equal, the F-test statistic should be close to 1.0. However, if the variances are not equal, the F-test statistic could be larger or smaller than 1.0 depending on which population has the larger variance.

Question 6

One of the major automobile makers has developed two new engines.At question is whether the two engines have the same variability with respect to miles per gallon.To test this,the following information is available:
  Based on this situation and the information provided,the test statistic is 1.2118.

Accepted Answer

The answer of One of the major automobile makers has...

Question 7

A frozen food company that makes burritos currently has employees making burritos by hand.It is considering purchasing equipment to automate the process and wants to determine if the automated process would result in lower variability of burrito weights.It takes a random sample from each process as shown below.
  To conduct a hypothesis test using a 0.05 level of significance,the critical value is 3.347.

Accepted Answer

The answer of A frozen food company that makes burritos...

Question 8

One of the major automobile makers has developed two new engines.At question is whether the two engines have the same variability with respect to miles per gallon.To test this using a significance level equal to 0.10,the following information is available:
  Based on this situation and the information provided,the critical value is F = 4.147 .

Accepted Answer

Based on the given information, the critical value for a significance level of 0.10 and 2 degrees of freedom for the numerator and 22 degrees of freedom for the denominator is indeed 4.147. Therefore, the statement is true.

Question 9

The logic behind the F-test for testing whether two populations have equal variances is to determine whether sample variances computed from random samples selected from the two populations differ due to sampling error,or whether the difference is more than can be attributed to sampling error alone,in which case,we conclude that the populations have different variances.

Accepted Answer

This is the correct logic behind the F-test for testing whether two populations have equal variances.

Question 10

One of the key quality characteristics in many service environments is that the variation in service time be reasonably small.Recently,a major amusement park company initiated a new line system at one of its parks.It then wished to compare this new system with the old system in place at a comparable park in another state.At issue is whether the standard deviation in waiting time is less under the new line system than under the old line system.The following information was collected:
  Assuming that it wishes to conduct the test using a 0.05 level of significance,the test statistic will be  .

Accepted Answer

The question mentions that the company wishes to conduct the test using a 0.05 level of significance, which is the standard level used in hypothesis testing. The test statistic is calculated using the formula provided, and the critical value for a two-tailed test at a significance level of 0.05 with 31 degrees of freedom (n-1) is approximately 2.039. The calculated test statistic of -2.14 falls outside of the range of the critical value, indicating that we can reject the null hypothesis that the standard deviation of waiting time is the same under both line systems in favor of the alternative hypothesis that the new line system has a smaller standard deviation of waiting time. Therefore, the statement is true.

Question 11

A two-tailed test for two population variances could have a null hypothesis like the following: H₀ : =

Accepted Answer

This is a valid null hypothesis for a two-tailed test for two population variances. The null hypothesis states that there is no significant difference between the variances of two populations.

Question 12

If a one-tailed F-test is employed when testing a null hypothesis about two population variances,the test statistic is an F-value formed by taking the ratio of the two sample variances so that the sample variance predicted to be larger is placed in the numerator.

Accepted Answer

This statement is true. When conducting a one-tailed F-test to test a null hypothesis about two population variances, we use the F-distribution to calculate a test statistic. The test statistic is the ratio of the two sample variances, with the larger variance placed in the numerator to obtain a value greater than one. The reason for using the larger variance in the numerator is that we want to see if the ratio of variances is significantly greater than one, which indicates that one population has a larger variance than the other.

Question 13

The F-distribution can only have positive values.

Accepted Answer

The F-distribution can only have positive values because it is the ratio of two chi-squared distributions, which are always positive.

Question 14

A frozen food company that makes burritos currently has employees making burritos by hand.It is considering purchasing equipment to automate the process and wants to determine if the automated process would result in lower variability of burrito weights.It takes a random sample from each process as shown below.
  In conducting the hypothesis test,the test statistic is F = 1.375.

Accepted Answer

The answer of A frozen food company that makes burritos...

Question 15

One of the major automobile makers has developed two new engines.At question is whether the two engines have the same variability with respect to miles per gallon.To test this,the following information is available: Based on this situation and the information provided,the appropriate null and alternative hypotheses are: H₀ : ≠ H_a : =

Accepted Answer

The answer of One of the major automobile makers has...

Question 16

One of the key quality characteristics in many service environments is that the variation in service time be reasonably small.Recently,a major amusement park company initiated a new line system at one of its parks.It then wished to compare this new system with the old system in place at a comparable park in another state.At issue is whether the standard deviation in waiting time is less under the new line system than under the old line system.The following information was collected:
  Assuming that it wishes to conduct the test using a 0.05 level of significance,the null hypothesis should be rejected since the test statistic exceeds the F-critical value from the F-distribution table.

Accepted Answer

The answer of One of the key quality characteristics in...

Question 17

The null hypothesis that two population variances are equal will tend to be rejected if the ratio of the sample variances from each population is substantially larger than 1.0.

Accepted Answer

This statement is true. In a two-sample variance test, the F-statistic is calculated as the ratio of the sample variances. If this ratio is significantly larger than 1.0, it suggests that the variances of the two populations are not equal, leading to rejection of the null hypothesis.

Question 18

Because of the way the F-distribution is formed,all F-tests are one-tailed tests.

Accepted Answer

F-tests can be either one-tailed or two-tailed depending on the research question and hypothesis being tested. One-tailed tests are used when the research question or hypothesis is directional, while two-tailed tests are used when the hypothesis is non-directional. Therefore, the statement that all F-tests are one-tailed tests is false.

Question 19

A potato chip manufacturer has two packaging lines and wants to determine if the variances differ between the two lines.They take samples of n₁ = 10 bags from line 1 and n₂ = 8 bags from line 2.To perform the hypothesis test at the 0.05 level of significance,the critical value is F = 3.68.

Accepted Answer

The critical value for an F-test depends on the degrees of freedom for the numerator and denominator, which are (n1-1) and (n2-1) respectively. For df1 = 9 and df2 = 7 at the 0.05 significance level, the critical value is not 3.68.

Question 20

A frozen food company that makes burritos currently has employees making burritos by hand.It is considering purchasing equipment to automate the process and wants to determine if the automated process would result in lower variability of burrito weights.To conduct a hypothesis test using a 0.05 level of significance,the proper format for the null and alternative hypotheses is (where the current by-hand process is process 1 and the automated process is process 2). H₀ : ≤ H_a : >

Accepted Answer

The answer of A frozen food company that makes burritos...

Quiz 11: Hypothesis Tests and Estimation for Population Variances

In a test for determining whether two population variances are the same or different,the larger the sample sizes from the two populations,the lower will be the chance of making a Type I statistical error.

A first step in testing whether two populations have the same mean value using the t-distribution is to use the chi-square distribution to test whether the populations have equal variances.

In a two-tailed hypothesis test involving two population variances,if the null hypothesis is true then the F-test statistic should be approximately equal to 1.0.

One of the major automobile makers has developed two new engines.At question is whether the two engines have the same variability with respect to miles per gallon.To test this,the following information is available: Based on this situation and the information provided,the test statistic is 1.2118.

A two-tailed test for two population variances could have a null hypothesis like the following: H0 : =

If a one-tailed F-test is employed when testing a null hypothesis about two population variances,the test statistic is an F-value formed by taking the ratio of the two sample variances so that the sample variance predicted to be larger is placed in the numerator.

The F-distribution can only have positive values.

The null hypothesis that two population variances are equal will tend to be rejected if the ratio of the sample variances from each population is substantially larger than 1.0.

Because of the way the F-distribution is formed,all F-tests are one-tailed tests.

A potato chip manufacturer has two packaging lines and wants to determine if the variances differ between the two lines.They take samples of n1 = 10 bags from line 1 and n2 = 8 bags from line 2.To perform the hypothesis test at the 0.05 level of significance,the critical value is F = 3.68.

A two-tailed test for two population variances could have a null hypothesis like the following: H₀ : =

A potato chip manufacturer has two packaging lines and wants to determine if the variances differ between the two lines.They take samples of n₁ = 10 bags from line 1 and n₂ = 8 bags from line 2.To perform the hypothesis test at the 0.05 level of significance,the critical value is F = 3.68.