Exam 11: Two-Sample Tests of Hypothesis

If two independent samples of size 10 with unequal standard deviations are used to test the difference between the means, the degrees of freedom for a t-statistic are 18.

If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations, the degrees of freedom are computed as (n₁)(n₂) - 1.

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 test statistic?

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, the variances are pooled to compute the best estimated variance.

If we are testing for the difference between two population proportions, it is assumed that the two populations follow the ________________ distribution.

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 value of calculated t?

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. This example is what type of test?

A company is researching the effectiveness of a new web site design to decrease the time to access a website. Five web site users were randomly selected and their times (in seconds) to access the web site with the old and new designs were recorded. The results follow. For a 0.01 significance level, what is the critical value?

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 null hypothesis?

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? If you use the 5% level of significance, what is the critical t value?

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: To test that the two groups of customers have equal savings rates, what is the critical value of z using $\alpha$ = 0.05? ___________

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. For a 0.05 significance level, what is the decision regarding the hypothesis that the training was effective in improving customer relationships?

The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the computed value of the test statistic?

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? Test the hypothesis with a 0.01 significance level. What is our decision? _______________

A company is researching the effectiveness of a new web site design to decrease the time to access a website. Five web site users were randomly selected and their times (in seconds) to access the web site with the old and new designs were recorded. The results follow. What is the value of the test statistic?

When is it appropriate to use the paired difference t-test?

A statistics professor wants to compare grades in two different classes of the same course. This is an example of _________ populations.

If two dependent samples of size 20 are used to test the difference between the means, the degrees of freedom for a t-statistic are 19.

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. What is the value of the test statistic?

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: If the population standard deviations are unknown and assumed unequal, what are the degrees of freedom?