Exam 11: Inferences About Population Variances

The standard deviation of the ages of a sample of 16 executives from the northern states was 8.2 years; while the standard deviation of the ages of a sample of 25 executives from the southern states was 12.8 years. At $\alpha$ = 0.1, test to see if there is any difference in the standard deviations of the ages of all the northern and southern executives.

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the

Exhibit 11-8 -Refer to Exhibit 11-8. The p-value is

The bottler of a certain soft drink claims their equipment to be accurate and that the variance of all filled bottles is 0.05 or less. The null hypothesis in a test to confirm the claim would be written as

A random sample of 41 scores of students taking the ACT test showed a standard deviation of 8 points. Provide a 98% confidence interval estimate for the standard deviation of all the ACT test scores.

ACT scores of a sample of UTC students are shown below. a.Compute the mean and the variance. b.At 95% confidence, test to determine whether or not the variance of the ACT scores of the population of UTC students is significantly more than 8.

Exhibit 11-3 The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounces. We are interested in testing to determine whether the variance of the population is significantly more than 0.003. -Refer to Exhibit 11-3. The test statistic is

Exhibit 11-1 Last year, the standard deviation of the ages of the students at UA was 1.8 years. Recently, a sample of 61 students had a standard deviation of 2.1 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA. -Refer to Exhibit 11-1. The test statistic is

Student advisors are interested in determining if the variances of the grades of day students and night students are the same. The following samples are drawn: Test the equality of the variances of the populations at 95% confidence.

Exhibit 11-2 We are interested in determining whether or not the variances of the sales at two music stores (A and B) are equal. A sample of 26 days of sales at store A has a sample standard deviation of 30 while a sample of 16 days of sales from store B has a sample standard deviation of 20. -Refer to Exhibit 11-2. The test statistic is

The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a standard deviation of 4 minutes. A 95% confidence interval estimate for the variance of service times for all their new automobiles is

We are interested in testing whether the variance of a population is significantly more than 625. The null hypothesis for this test is

A random sample of 31 charge sales showed a sample standard deviation of $50. A 90% confidence interval estimate of the population standard deviation is

The value of F_.05 with 8 numerator and 19 denominator degrees of freedom is

The critical value of F at 95% confidence when there is a sample size of 21 for the sample with the smaller variance, and there is a sample size of 9 for the sample with the larger sample variance is

Exhibit 11-5 -Refer to Exhibit 11-5. The null hypothesis

The sampling distribution of the quantity (n-1)s²/ $\sigma$ ²is the

Exhibit 11-2 We are interested in determining whether or not the variances of the sales at two music stores (A and B) are equal. A sample of 26 days of sales at store A has a sample standard deviation of 30 while a sample of 16 days of sales from store B has a sample standard deviation of 20. -Refer to Exhibit 11-2. The p-value for this test is

The symbol used for the variance of the sample is

Exhibit 11-1 Last year, the standard deviation of the ages of the students at UA was 1.8 years. Recently, a sample of 61 students had a standard deviation of 2.1 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA. -Refer to Exhibit 11-1. At 95% confidence the null hypothesis