Exam 10: Comparisons Involving Means, Experimental Design and Analysis of Variance

Consider the following results for two samples randomly taken from two populations. a.What are the degrees of freedom for the t distribution? b.At 95% confidence, compute the margin of error. c.Develop a 95% confidence interval for the difference between the two population means.

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. -Refer to Exhibit 10-2. Based on the results of question 18, the

Exhibit 10-15 The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations. -Refer to Exhibit 10-15. The mean square between treatments (MSTR) is

Information regarding the ACT scores of samples of students in three different majors is given below. a.Compute the overall sample mean. b.Set up the ANOVA table for this problem including the test statistic. c.At 95% confidence, determine the critical value of F. d.Using the critical value approach, test to determine whether there is a significant difference in the means of the three populations. e. Determine the p-value and use it for the test.

The following information was obtained from matched samples regarding the productivity of four individuals using two different methods of production. Let d = Method 1 - Method 2. Is there a significant difference between the productivity of the two methods? Let $\alpha$ = 0.05.

We are interested in testing the following hypotheses. H₀: $\mu$ ₁- $\mu$ ₂ = 0 H_a: $\mu$ ₁- $\mu$ ₂ ? 0 The test statistic Z is computed to be 1.85. The p-value for this test is

Nancy, Inc. has three stores located in three different areas. Random samples of the sales of the three stores (In $1,000) are shown below. a.Compute the overall mean. b.At 95% confidence, test to see if there is a significant difference in the average sales of the three stores.

In order to estimate the difference between the yearly incomes of marketing managers in the East and West of the United States, the following information was gathered. a.Develop an interval estimate for the difference between the average yearly incomes of the marketing managers in the East and West. Use $\alpha$ = 0.05. b.At 95% confidence, use the p-value approach and test to determine if the average yearly income of marketing managers in the East is significantly different from the West.

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. -Refer to Exhibit 10-1. The p-value is

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. -Refer to Exhibit 10-3. The p-value for the difference between the two population means is

Exhibit 10-13 Part of an ANOVA table is shown below. -Refer to Exhibit 10-13. If at 95% confidence, we want to determine whether or not the means of the populations are equal, the p-value is

The following information regarding the ages of full-time and part-time students are given. Using the following data, develop an interval estimate for the difference between the mean ages of the two populations. Use a 5% level of significance. The degrees of freedom for the t distribution is 106.

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom for the critical value of F are

Consider the following hypothesis test: The following results are for two independent samples taken from two populations. a.Determine the degrees of freedom for the t distribution. b.Compute the test statistic. c.Determine the p-value and test the above hypotheses.

In order to improve the grades of students at UTC, several incentive programs have been introduced. Results of random samples of grades from after and before the incentive programs are given below. a.Give the hypotheses. b.Compute the test statistic. c.At a 0.1 level of significance, test to determine whether the incentive programs have significantly increased the average grades.

Allied Corporation is trying to determine whether to purchase Machine A or B. It has leased the two machines for a month. A random sample of 5 employees has been taken. These employees have gone through a training session on both machines. Below you are given information on their productivity rate on both machines. (Let the difference d = Machine A - Machine B.) a.State the null and alternative hypotheses for a two-tailed test. b.Find the mean and standard deviation for the difference. c.Compute the test statistic. d.Test the null hypothesis stated in Part a at the 10% level.

Exhibit 10-5 The following information was obtained from matched samples. -Refer to Exhibit 10-5. The 95% confidence interval for the difference between the two population means is

Exhibit 10-15 The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations. -Refer to Exhibit 10-15. The conclusion of the test is that the means

Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n₁ = 25 and n₂ = 35. The correct distribution to use is the

The following information regarding the yearly salaries (in $1,000) of CEO's in 2010 and 2009 are provided. a.At 95% confidence, perform a test to determine if there has been a significant increase in the salaries of CEO's. Use the Critical Value Approach. b.Compute the p-value.