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 here. 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?

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?

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 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 are shown here. For a 0.01 significance level,what is the decision regarding the hypothesis that the training was effective in improving customer relationships?

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 ________.

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and a 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 are shown here. For a 0.05 significance level,what is the critical value?

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and a 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 are shown here. This analysis is an example of ________.

A recent study focused on the number of times men and women send a Twitter message in a day. The sample information is summarized here. At the 0.01 significance level,we ask if there is 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?

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?

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

Use the following table to determine whether or not there is a significant difference between the average hourly wages at two manufacturing companies. What is the test statistic for the difference between the means?

The results of a mathematics placement exam at two different campuses of Mercy College follow: 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 a paired sample.

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and a 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 are shown here. For a 0.05 significance level,what is the decision regarding the hypothesis that the training was effective in improving customer relationships?

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 are shown here. What is the value of the test statistic?

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. We would like to determine if the LIFO method results in a lower cost of inventory than the FIFO method. What is the null hypothesis?

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. We would like to determine if the LIFO method results in a lower cost of inventory than the FIFO method. If you use the 5% level of significance,what is the critical t-value?

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?

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 here. 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?

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 cannot be true? Assume the population standard deviations are equal.