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

The Ahmadi Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below. a.State the null and alternative hypotheses. b.Construct an ANOVA table. c.As the statistical consultant to Ahmadi, what would you advise them? Use a .05 level of significance. Use both the critical and p-value approaches.

Exhibit 10-10 -Refer to Exhibit 10-10. The mean square within treatments (MSE) equals

Exhibit 10-12 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. -Refer to Exhibit 10-12. The mean square between treatments (MSTR) is

At $\alpha$ = 0.05, test to determine if the means of the three populations (from which the following samples are selected) are equal. Use both the critical and p-value approaches.

If a hypothesis is rejected at 95% confidence, it

Information regarding the starting salaries (in $1,000) of samples of students in four different majors is given below. Majors 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.

Samples of employees of Companies A and B provided the following information regarding the ages of employees. Develop a 97% confidence interval for the difference between the average ages of the employees of the two companies.

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. -Refer to Exhibit 10-9. The mean for the differences is

Test scores on a standardized test from samples of students from two universities are given below. Provide a 98% confidence interval estimate for the difference between the test scores of the two universities.

Exhibit 10-10 -Refer to Exhibit 10-10. The null hypothesis is to be tested at the 5% level of significance. The p-value is

We are interested in testing the following hypotheses. H₀: $\mu$ ₁- $\mu$ ₂ $\ge$ 0 H_a: $\mu$ ₁- $\mu$ ₂ < 0 Based on 40 degrees of freedom, the test statistic t is computed to be 2.423. The p-value for this test is

Exhibit 10-10 -Refer to Exhibit 10-10. The mean square between treatments (MSTR) equals

Three different brands of tires were compared for wear characteristics. From each brand of tire, ten tires were randomly selected and subjected to standard wear-testing procedures. The average mileage obtained for each brand of tire and sample variances (both in 1,000 miles) are shown below. At 95% confidence, test to see if there is a significant difference in the average mileage of the three brands.

Exhibit 10-14 Part of an ANOVA table is shown below. -Refer to Exhibit 10-14. The conclusion of the test is that the means

In order to compare the life expectancies of three different brands of tires, ten tires of each brand were randomly selected and were subjected to standard wear testing procedures. Information regarding the three brands is shown below. Use the above data and test to see if the mean mileage for all three brands of tires is the same. Let $\alpha$ = 0.05. Use both the critical value and p-value approaches.

MNM, Inc. has three stores located in three different areas. Random samples of the daily sales of the three stores (in $1,000) are shown below. At 95% confidence, test to see if there is a significant difference in the average sales of the three stores. Use both the critical and p-value approaches.

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. -Refer to Exhibit 10-4. The point estimate for the difference between the means of the two populations is

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. The point estimate for the difference between the means of the two populations is

An ANOVA procedure is used for data obtained from four populations. Four samples, each comprised of 30 observations, were taken from the four populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

In a completely randomized experimental design, 14 experimental units were used for each of the 5 levels of the factor (i.e., 5 treatments). Fill in the blanks in the following ANOVA table.