Exam 11: Two-Sample Tests of Hypothesis

If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, then the test has ________ degrees of freedom.

Consider independent simple random samples that are taken to test the difference between the means of two populations. The variances of the populations are unknown, but are assumed to be equal. The sample sizes of each population are n₁ = 37 and n₂ = 45. The appropriate distribution to use is the:

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. What is the null hypothesis?

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

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. What is the null hypothesis?

When testing the null hypothesis that two population means are equal, the hypothesized difference between the population means is ________________.

A recent study focused on the number of times men and women send a Twitter message in a day. The sample 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 test statistic for this hypothesis?

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? This example is what type of test?

If samples taken from two populations are dependent, then a test of ______ differences is applied.

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

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. What is the alternative 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 are assumed equal. This example is what type of test?

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences they computed (post-training survey score - pre-training survey score). 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?

A study by a bank compared the mean 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 as follows. Assuming that the financial officer wants to show that there is a difference in the average savings balance between the two classes of depositors, the null hypothesis is ____________.

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

Use the following table to determine whether or not there is a significant difference between the average hourly wages at two manufacturing companies. The p-value is ______.

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 α = 0.05?

The paired t test is especially appropriate when the two samples are ________.

The following table shows sample salary information for employees with bachelor's and associate degrees for a large company in the Southeast United States. The point estimate of the difference between the means of the two populations is ______.