Exam 11: Inferences About Population Variances

The sampling distribution of the $\frac { ( n - 1 ) s ^ { 2 } } { \sigma ^ { 2 } }$ quantity is the _____.

A sample of 61 items provided a sample mean of 932, a sample mode of 900, and a sample standard deviation of 11. Test the following hypotheses using α = .05. What is your conclusion? ​ H₀: α² ≤ 80 H_a: α² > 80

The 99% confidence interval estimate for a population variance when a sample standard deviation of 12 is obtained from a sample of 10 items is _____.

The χ² value for a one-tailed test (lower tail) when the level of significance is .1 and the sample size is 15 is _____.

At α = .1, test to see if the population variances from which the following samples were drawn are equal. Group $1 \quad$ Group 2 =21 =19 =18 =16 ​

The 90% confidence interval estimate for a population standard deviation when a sample variance of 50 is obtained from a sample of 15 items 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 _____.

A sample of 28 elements is selected to estimate a 95% confidence interval for the variance of the population. The χ² values to be used for this interval estimation are _____.

A sample of 20 cans of tomato juice showed a standard deviation of 0.4 ounce. A 95% confidence interval estimate of the variance for the population is _____.

To avoid the problem of not having access to tables of the F distribution with values given for the lower tail when a two-tailed test is required, let the smaller sample variance be _____.

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

To avoid the problem of not having access to tables of F distribution with values given for the lower tail, the numerator of the test statistic should be the one with the _____.

The specifications for the filling of soft drink bottles is a variance of .05 (ounces)². A sample of 20 bottles of soft drink showed the following results: 12.03 12.01 11.89 12.15 12.23 11.97 12.10 11.85 12.33 12.02 11.96 12.00 11.82 12.02 11.99 11.96 11.83 11.84 12.21 12.38 At a 5% level of significance, use Excel to determine whether or not the variance of the population is significantly different from .05.

A sample of 16 students showed that the variance in the number of hours they spend studying is 25. At a 5% level of significance, test to see if the variance of the population is significantly different from 30.

The symbol used for the variance of the sample is _____.

Do the following data indicate that the variance of the population from which this sample has been drawn is significantly more than 12? Use α = .05. 16 12 21 10 13 18

A sample of 30 items provided a sample mean of 28 and a sample standard deviation of 6. Test the following hypotheses using α = .05. What is your conclusion? ​ H₀: σ² ≤ 25 H_a: σ² > 25

The data below shows samples of annual salaries (in $1000s) for accountants in two different firms. Company A Company B 74.8 83.3 78.2 65.7 69.9 82.1 84 78.5 65.7 69.7 66.8 77.7 72.1 66.7 77.4 78.4 79.3 79.2 69.1 80.1 74.9 69.8 Use Excel to determine whether the variance in salaries in Company A differs from that of Company B. Use a .10 level of significance.

A lumber company has claimed that the standard deviation for the lengths of its six-foot boards is 0.5 inch or less. To test its claim, a random sample of 17 six-foot boards is selected, and it is determined that the standard deviation of the sample is .43. Do the results of the sample support the company's claim? Use α = .1.

In Excel, which of the following functions is used to conduct a hypothesis test (using the p-value) for a population variance?