Exam 13: Experimental Design and Analysis of Variance

In order to test to see if there is any significant difference in the mean number of units produced per week by each of three production methods, the following data were collected. (Please note that the sample sizes are not equal.) a.Compute . b.At the $\alpha$ = 0.05 level of significance, is there any difference in the mean number of units produced per week by each method? Show the complete ANOVA table. Use both the critical and p-value approaches.

Which of the following is not a required assumption for the analysis of variance?

In order to compare the life expectancies of three different brands of printers, eight printers of each brand were randomly selected. Information regarding the three brands is shown below. a.Compute the overall mean . b.State the null and alternative hypotheses to be tested. c.Show the complete ANOVA table for this test including the test statistic. d.The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude? e.Determine the p-value and use it for the test.

Ten observations were selected from each of 3 populations, and an analysis of variance was performed on the data. The following are the results: a.Using $\alpha$ = .05, test to see if there is a significant difference among the means of the three populations. b.If in Part a you concluded that at least one mean is different from the others, determine which mean is different. The three sample means are

You are given an ANOVA table below with some missing entries. a. State the null and alternative hypotheses. b. Compute the sum of squares between treatments. c. Compute the mean square due to error. d. Compute the total sum of squares. e. Compute the test statistic f.f. Test the null hypothesis stated in Part a at the 1% level of significance. Be sure to state your conclusion.

Individuals were randomly assigned to three different production processes. The hourly units of production for the three processes are shown below. Use the analysis of variance procedure with $\alpha$ = 0.05 to determine if there is a significant difference in the mean hourly units of production for the three types of production processes. Use both the critical and p-value approaches.

The test scores for selected samples of sociology students who took the course from three different instructors are shown below. At $\alpha$ = 0.05, test to see if there is a significant difference among the averages of the three groups. Use both the critical value and p-value approaches.

In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is

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.

Three different models of automobiles (A, B, and C) were compared for gasoline consumption. For each model of car, fifteen cars were randomly selected and subjected to standard driving procedures. The average miles/gallon obtained for each model of car and sample standard deviations are shown below. Use the above data and test to see if the mean gasoline consumption for all three models of cars is the same. Let $\alpha$ = 0.05, and use both the critical and p-value approaches.

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

The process of allocating the total sum of squares and degrees of freedom is called

Exhibit 13-1 -Refer to Exhibit 13-1. The null hypothesis

In a completely randomized design involving three treatments, the following information is provided: The overall mean for all the treatments is

The marketing department of a company has designed three different boxes for its product. It wants to determine which box will produce the largest amount of sales. Each box will be test marketed in five different stores for a period of a month. Below you are given the information on sales. a.State the null and alternative hypotheses. b.Construct an ANOVA table. c.What conclusion do you draw? d.Use Fisher's LSD procedure and determine which mean (if any) is different from the others. Let $\alpha$ = 0.01.