Exam 11: Two-Sample Tests of Hypothesis

Two samples, one of size 14 and the second of size 13, are selected to test the difference between two population means. How many degrees of freedom are used to find the critical value? Assume the population standard deviations are equal.

A committee studying employer-employee relations proposed that each employee would rate his or her immediate supervisor and in turn the supervisor would rate each employee. To find reactions regarding the proposal, 120 office personnel and 160 plant personnel were selected at random. Seventy-eight of the office personnel and 90 of the plant personnel were in favor of the proposal. What is the pooled estimate of the population proportion?

A hypothesis tests that two population means are equal. A sample of 10 with a standard deviation of 5 is selected from the first population and a sample of 15 with a standard deviation of 5 from the second population. Testing the claim at the 0.01 level, what is the critical value? Assume unequal standard deviations.

A study by a bank compared the average savings of customers who were depositors for three years or less, with those who had been depositors for more than three years. The results of a sample are: Assuming that the financial officer wants to show that there is a difference in the average savings balance between the two classes of depositors, what is the null hypothesis? _____________________

How is a pooled estimate of the population proportion represented?

A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is calculated. The results are presented below. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. Assume that the population standard deviations are equal. What is the alternate hypothesis?

A committee studying employer-employee relations proposed that each employee would rate his or her immediate supervisor and in turn the supervisor would rate each employee. To find reactions regarding the proposal, 120 office personnel and 160 plant personnel were selected at random. Seventy-eight of the office personnel and 90 of the plant personnel were in favor of the proposal. To test the hypothesis that the population proportions are equal, what is the critical value using the 0.05 level of significance?

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $ thousands) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? What are the degrees of freedom?

When testing the difference between two dependent population means, the test statistic is based on a

Of 250 adults who tried a new multi-grain cereal, "Wow!", 187 rated it excellent; of 100 children sampled, 66 rated it excellent. Using the 0.1 significance level and the alternate hypothesis $\pi$ ₁ not equal to $\pi$ ₂ , what is the null hypothesis?

For hypotheses that compare two population means, what test statistic is used when the population standard deviations are unknown?

Suppose we test the difference between two proportions at the 0.05 level of significance. If the z test statistic is -1.07, what is our decision?

Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $ thousands) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? What is the decision at the 5% level of significance?

Which condition must be met to conduct a test for the difference in two sample means using a z-statistic?

What is the critical value of t for the claim that the difference of two means is less than zero with a = 0.025 and sample sizes of nine and seven? Assume equal population standard deviations. _________

A financial planner wants to compare the yield of income and growth mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income and 40 growth funds. The mean increase for a two-year period for the income funds is $900. For the growth funds the mean increase is $875. Income funds have a sample standard deviation of $35; growth funds have a sample standard deviation of $45. Assume that the population standard deviations are equal. At the 0.05 significance level, is there a difference in the mean yields of the two funds? What is the null hypothesis? __________________

To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions? What is the pooled estimate of the population proportion? _______

When testing the difference between two population means, the hypothesized difference is _______________.

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. Seven customers were randomly selected and completed both surveys. The results follow. This analysis is an example of

When testing for a difference between the means of two dependent samples n₁ and n₂ are _______________.