Chapter 11

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. Sample Size Sample Mean Population Standard Deviation Men 25 23 5 Women 30 28 10 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?

z-statistic

Two samples, one of size 14 and the second of size 13, are selected to test the difference between two population means. How many degrees of freedom are used to find the critical value? Assume the population standard deviations are equal.

25

se the following table to determine whether or not there is a significant difference between the average hourly wages at two manufacturing companies. Manufacture 1 Manufacturer 2 n1 = 81 n2 = 64 = $15.80 = $15.00 σ1 = $3.00 σ2 = $2.25 What is the test statistic for the difference between the means?

1.83

The results of a mathematics placement exam at two different campuses of Mercy College follow: Campus Sample Size Sample Mean Population Standard Deviation 1 330 33 8 2 310 31 7 What is the computed value of the test statistic?

3.37

The following table shows sample salary information for employees with bachelor's and associate's degrees for a large company in the Southeast United States. Bachelor's Associate's Sample size (n) 81 49 Sample mean salary (in $1,000) 60 51 Population variance (σ2) 175 90

9

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?

25

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. Process A Process B Sample mean 2.0 3.0 Standard deviation 1.0 0.5 Sample size 12 14 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?

H1: µA ≠ µB

Use the following table to determine whether or not there is a significant difference between the average hourly wages at two manufacturing companies. Manufacture 1 Manufacture 2 n1 = 81 n2 = 64 = $15.80 = $15.00 σ1 = $3.00 σ2 = $2.25 The p-value is ________.

0.0336

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here. Sample Size Sample Mean Population Standard Deviation Men 25 23 5 Women 30 28 10 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 p-value for this hypothesis test?

0.0164

Which condition must be met to conduct a test for the difference in two sample means using a z-statistic?

The two population standard deviations must be known.

Campus Sample Size Sample Mean Population Standard Deviation 1 330 33 8 2 310 31 7 Given that the two population standard deviations are known, what is the p-value?

0.0

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 paired t-test

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

standard deviation of the differences

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.

n1 = 11; n2 = 13

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

the population variances are assumed equal but unknown

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

the sum of the two population variances

For a hypothesis comparing two population means, H0: μ1 ≤ μ2, 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.

+1.711

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 shown here. Edne 8 7 6 9 7 5 Orno 10 7 11 9 12 14 9 8 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.

+1.782

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here. Sample Size Sample Mean Population Standard Deviation Men 25 23 5 Women 30 28 10 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 value of the test statistic for this hypothesis test?

2.40

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. Process A Process B Sample mean 2.0 3.0 Standard deviation 1.0 0.5 Sample size 12 14 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?

24

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. Process A Process B Sample mean 2.0 3.0 Standard deviation 1.0 0.5 Sample size 12 14 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?

A two-sample test of means

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here. Sample Size Sample Mean Population Standard Deviation Men 25 23 5 Women 30 28 10 At the 0.01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day? Based on the p-value, what is your conclusion?

Fail to reject the null hypothesis.

When testing the hypothesized equality of two population means, the implied null hypothesis is ________.

H0: µ1 − µ2 = 0

The results of a mathematics placement exam at two different campuses of Mercy College follow: Campus Sample Size Sample Mean Population Standard Deviation 1 330 33 8 2 310 31 7 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?

H0: µ1 ≤ µ2

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. Process A Process B Sample mean 2.0 3.0 Standard deviation 1.0 0.5 Sample size 12 14 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?

H0: µA = µB

The results of a mathematics placement exam at two different campuses of Mercy College follow: Campus Sample Size Sample Mean Population Standard Deviation 1 330 33 8 2 310 31 7 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?

H1: µ1 > µ2

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. Process A Process B Sample mean 2.0 3.0 Standard deviation 1.0 0.5 Sample size 12 14 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?

Reject the null hypothesis and conclude the means are different.

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

When two dependent samples are compared

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 ________.

t-distribution with df = 80

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

±2.17

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. Process A Process B Sample mean 2.0 3.0 Standard deviation 1.0 0.5 Sample size 12 14 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?

±2.797

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. Process A Process B Sample mean 2.0 3.0 Standard deviation 1.0 0.5 Sample size 12 14 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 computed value of t?

−3.299