Exam 11: Two-Sample Tests of Hypothesis

When testing for a difference between the means of two dependent samples the sample test statistic is a _____________.

If two dependent samples of size 100 are used to test the difference between the means, the degrees of freedom for a t-statistic are ____.

If the null hypothesis states that there is no difference between the mean income of males and the mean income of females, then the test is one-tailed.

A recent study focused on the amount of money single men and women save monthly. The information is summarized below. Assume that the population standard deviations are equal. At the .01 significance level, do women save more money than men?

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 computed value of t?

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. We test the hypothesis that the population proportions are equal with a 0.05 significance level. What is our decision? _______________

The results of a mathematics placement exam at two different campuses of Mercy College follow: Given that the two population standard deviations are known, what is the p-value?

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized below. At the .01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day? What is the value of the test statistic for this hypothesis test?

The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the alternative hypothesis if we want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2?

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: What is the p-value for a two-tailed test? _____

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 computed value of the test statistic? ______________

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 null hypothesis?

If a hypothesis states that one population mean is greater than another population mean, then the test is _______________.

When can a paired-t test be used to test a hypothesis of no difference between population means?

What is the critical value of t for a two-tail test of the difference of two means, a level of significance of 0.10 and sample sizes of seven and fifteen? Assume equal population standard deviations. _________

For hypotheses that compare two population means, when is a pooled variance used?

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 critical t value at the 1% level of significance?

The results of a mathematics placement exam at two different campuses of Mercy College follow: What is the null hypothesis if we want to test the hypothesis that the mean score on Campus 1 is higher than on Campus 2?

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: What is the computed 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? What is the proportion of sales made in Region B? ______