Exam 11: Two-Sample Tests of 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. The results follow. Let α = 0.05. Is the mean time to access the new website design shorter, or is (time for the old design - time for the new design) greater than zero? Express your answer in terms of the null hypothesis.

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?

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

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

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 critical value?

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, do women save more money than men? What is the test statistic for this hypothesis?

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

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.

For a hypothesis comparing two population means, H₀: μ₁ ≤ μ_2, what is the critical value for a one-tailed hypothesis test, using a 5% significance level, with both sample sizes equal to 13? Assume the population standard deviations are equal.

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.

For a hypothesis test comparing two population means, the combined degrees of freedom are 24. Which of the following statements about the two sample sizes is NOT true? Assume the population standard deviations are equal.

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 are the degrees of freedom?

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. The results follow. What is the value of the test statistic to test for differences in the times?

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 p-value for this hypothesis test?

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

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. What is the value of the test statistic?

We test for a hypothesized difference between two population means: H₀: μ₁ = μ₂. The population standard deviations are unknown but assumed equal. The number of observations in the first sample is 15, and 12 in the second sample. How many degrees of freedom are associated with the critical value?

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 null hypothesis?

When the population standard deviations are equal but unknown, a test for the differences between two populations assumes that the populations are _____________ distributed.