Exam 11: Two-Sample Tests of Hypothesis

The net weights (in grams) of a sample of bottles filled by a machine manufactured by Edne, and the net weights of a sample filled by a similar machine manufactured by Orno, Inc., are: Testing the claim at the 0.05 level that the mean weight of the bottles filled by the Orno machine is greater than the mean weight of the bottles filled by the Edne machine, what is the critical value? Assume equal standard deviations for both samples.

Assuming the population variances are known, the population variance of the difference between two means is _____________.

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

Twenty randomly selected statistics students were given 15 multiple-choice questions and 15 open-ended questions, all on the same material. The professor was interested in determining if students scored higher on the multiple-choice questions. This experiment is an example of ________________.

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 measured in millimeters. The results are presented next. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but assumed equal. What is the critical t value at the 1% level of significance?

A recent study focused on the amount of money single men and women save monthly. The information is summarized next. Assume that the population standard deviations are equal. At the .01 significance level, what is the conclusion about the way women and men save?

Accounting procedures allow a business to evaluate their inventory costs based on two methods: LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $000s) for five products with the LIFO and FIFO methods. To analyze the difference, they computed (FIFO - LIFO) for each product. Based on the following results, does the LIFO method result in a lower cost of inventory than the FIFO method? What is the alternate hypothesis?

A company is researching the effectiveness of a new website design to decrease the time to access a website. Five website users were randomly selected, and their times (in seconds) to access the website with the old and new designs were recorded. To compare the times, they computed (new website design time - old website design time). The results follow. For a 0.01 significance level, what is the decision regarding the hypothesis that the training was effective in improving customer relationships?

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized next. 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?

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?

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 p-value for a two-tailed test?

If the null hypothesis that two means are equal is true, where will 97% of the computed z values lie between?

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?

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?

If the null hypothesis states that there is no difference between the mean net income of retail stores in Chicago and New York City, then the test is two-tailed.

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 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 measured in millimeters. The results are presented next. The researcher is interested in determining whether there is evidence that the two processes yield different average errors. The population standard deviations are unknown but are assumed equal. If we test the null hypothesis at the 1% level of significance, what is the decision?

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.