Exam 11: Two-Sample Tests of Hypothesis

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 alternate 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: What is the computed test statistic? Round to two decimal places.

When independent samples are used to test for differences in the population means with equal but unknown population standard deviations, we _______ these sample standard deviations.

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?

When dependent samples are used to test for differences in the means, we compute paired differences.

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 p-value for the computed 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 ________________.

The paired difference test has ___________ degrees of freedom.

When dependent samples are used to test for differences in the means, we pool the sample variances.

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?

When independent samples with unknown but equal standard deviations are used to test for differences in the means, we pool the sample _________________.

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

Accounting procedures allow a business to evaluate its 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 value of calculated t?

Accounting procedures allow a business to evaluate its 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 decision at the 5% level of significance?

When testing the difference between two population means, the sample variances are pooled to estimate the population variance when ________________.

If we are testing for the difference between two population means, it is assumed that the sample observations from one population are independent of the sample observations from the other population.

In one class, a statistics professor wants to compare grades on the first and second exams. This is an example of ________________ observations.

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

When the population standard deviations are unknown, the purpose of pooling the sample variances when testing the difference between two populations is to ___________.

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.