Exam 13: Analysis of Variance and Experimental Design

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

Exhibit 13-5 Part of an ANOVA table is shown below. -Refer to Exhibit 13-5.The test statistic is

In the ANOVA,treatment refers to

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

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.

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.

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.

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

The mean square is the sum of squares divided by

Exhibit 13-3 To test whether or not there is a difference between treatments A,B,and C,a sample of 12 observations has been randomly assigned to the 3 treatments.You are given the results below. -Refer to Exhibit 13-3.The mean square between treatments (MSTR)equals

The three major automobile manufacturers have entered their cars in the Indianapolis 500 race.The speeds of the tested cars are given below. At $\alpha$ = .05,test to see if there is a significant difference in the average speeds of the cars of the auto manufacturers.Use both the critical and p-value approaches.

Exhibit 13-2 -Refer to Exhibit 13-2.The null hypothesis

The critical F value with 8 numerator and 29 denominator degrees of freedom at $\alpha$ = 0.01 is

The following are the results from a completely randomized design consisting of 3 treatments. a.Using $\alpha$ = .05,test to see if there is a significant difference among the means of the three populations.The sample sizes for the three treatments are equal. b.If in Part a you concluded that at least one mean is different from the others,determine which mean(s)is(are)different.The three sample means areUse Fisher's LSD procedure and let $\alpha$ = .05.

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

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.

Random samples of several days' sales of handguns per day in three different states are shown below.We are interested in determining whether or not there is a significant difference in the average sales of guns in the three states 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.

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is K,the mean square within treatments is

Employees of MNM Corporation are about to undergo a retraining program.Management is trying to determine which of three programs is the best.They believe that the effectiveness of the programs may be influenced by sex.A factorial experiment was designed.You are given the following information. a.Set up the ANOVA table. b.What advice would you give MNM? Use a .05 level of significance.

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. d.Use Fisher's LSD procedure and determine which population mean (if any)is different from the others.Let $\alpha$ = .05.