Exam 13: Analysis of Variance and Experimental Design

Part of an ANOVA table is shown below. a.Compute the missing values and fill in the blanks in the above table.Use $\alpha$ = .01 to determine if there is any significant difference among the means. b.How many groups have there been in this problem? c.What has been the total number of observations?

Information regarding the starting salaries (in $1,000)of samples of students in four 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 final examination grades of random samples of students from three different classes are shown below. At the $\alpha$ = .05 level of significance,is there any difference in the mean grades of the three classes?

Eight observations were selected from each of 3 populations (total of 24 observations),and an analysis of variance was performed on the data.The following are part of the results. Using $\alpha$ = .05,test to see if there is a significant difference among the means of the three populations.

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 null hypothesis for this ANOVA problem is

A factorial experiment involving 2 levels of factor A and 2 levels of factor B resulted in the following. Set up an ANOVA table and test for any significant main effect and any interaction effect.Use $\alpha$ = .05.

Guitars R.US has three stores located in three different areas.Random samples of the sales of the three stores (in $1000)are 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.

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 test statistic to test the null hypothesis equals

Carolina,Inc.has three stores located in three different areas.Random samples of the sales of the three stores (in $1,000)are shown below.Please note that the sample sizes are not equal. 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.Use both the critical value and p-value approaches.Show your complete work and the ANOVA table.

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

Exhibit 13-7 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 13-7.The number of degrees of freedom corresponding to between treatments is

For four populations,the population variances are assumed to be equal.Random samples from each population provide the following data. Using a .05 level of significance,test to see if the means for all four populations are the same.

The ANOVA procedure is a statistical approach for determining whether or not

Six observations were selected from each of three populations.The data obtained is shown below. Test at the $\alpha$ = 0.05 level to determine if there is a significant difference in the means of the three populations.Use both the critical value and the p-value approaches.

Exhibit 13-6 Part of an ANOVA table is shown below. -Refer to Exhibit 13-6.If at 95% confidence we want to determine whether or not the means of the populations are equal,the p-value is

In factorial designs,the response produced when the treatments of one factor interact with the treatments of another in influencing the response variable is known as

An experimental design where the experimental units are randomly assigned to the treatments is known as

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.

In an analysis of variance problem if SST = 120 and SSTR = 80,then SSE is

An experimental design that permits statistical conclusions about two or more factors is a