Exam 13: Experimental Design and Analysis of Variance

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

Six observations were selected from each of three populations. The data obtained are shown below. Sample 1 Sample 2 Sample 3 31 37 37 28 32 31 34 34 32 32 24 39 26 32 30 29 33 35 Test at α = .05 level to determine if there is a significant difference in the means of the three populations. ​

For four populations, the population variances are assumed to be equal. Random samples from each population provide the following data. Population Sample Size Sample Mean Sample Variance 1 11 40 23.4 2 11 35 21.6 3 11 39 25.2 4 11 37 24.6 Using a .05 level of significance, test to see if the means for all four populations are the same.

At α = .05, test to determine if the means of the three populations (from which the following samples are selected) are equal. Sample 1 Sample 2 Sample 3 60 84 60 78 78 57 72 93 69 66 81 66

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 _____.

Three universities administer the same comprehensive examination to the recipients of MS degrees in psychology. From each institution, a random sample of MS recipients was selected, and these recipients were then given the exam. The following table shows the scores of the students from each university. University A University B University C 89 60 81 95 95 70 75 89 90 92 80 78 99 66 77 At α = .01, test to see if there is any significant difference in the average scores of the students from the three universities. (Note that the sample sizes are not equal.) ​

An ANOVA procedure is used for data that were obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are _____.

A factorial experiment involving two levels of factor A and two levels of factor B resulted in the following. Factor B Factor A Level 1 Level 2 Level 1 14 18 16 12 Level 2 18 16 20 14 Use Excel and test for any significant main effect and any interaction effect. Use α = .05.

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

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 gender. A factorial experiment was designed. You are given the following information. Factor B: Gender Factor A: Program Male Female Program A 320 380 240 300 Program B 160 240 180 210 Program C 240 360 290 380 What advice would you give MNM? Use Excel and a .05 level of significance.

The independent variable of interest in an ANOVA procedure is called _____.

Three universities in your state decided to administer the same comprehensive examination to the recipients of MBA degrees from the three institutions. From each institution, MBA recipients were randomly selected and were given the test. The following table shows the scores of the students from each university. Northern University Central University Southern University 85 80 89 81 86 84 88 79 81 83 At α = .01, test to see if there is any significant difference in the average scores of the students from the three universities. (Note that the sample sizes are not equal.)

When an analysis of variance is performed on samples drawn from k populations, the mean square between treatments (MSTR) is _____.

Three universities in your state decided to administer the same comprehensive examination to the recipients of MBA degrees from the three institutions. From each institution, MBA recipients were randomly selected and were given the test. The following table shows the scores of the students from each university. Northern University Central University Southern University 75 85 80 80 89 81 84 86 84 85 88 79 81 83 At α = .01, test to see if there is any significant difference in the average scores of the students from the three universities. (Note that the sample sizes are not equal.)

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 _____.

Random samples of individuals from three different cities were asked how much time they spend per day watching television. The results (in minutes) for the three groups are shown below. City I City II City III 260 178 211 280 190 190 240 220 250 260 240 300 At α = .05, test to see if there is a significant difference in the averages of the three groups.

At α = .05, test to determine if the means of the three populations (from which the following samples are selected) are equal. Sample 1 Sample 2 Sample 3 60 84 60 78 78 57 72 93 69 66 81 66

In a completely randomized experimental design, 14 experimental units were used for each of the five levels of the factor (i.e., five treatments). Fill in the blanks in the following ANOVA table. Source of Variation Sum of Degrees of Mean F Squares Freedom Square Between treatments 1,500 \_\_\_\_? 800.00 \_\_\_\_? Within treatments (Error) \_\_\_\_? \_\_\_\_? \_\_\_\_? Total 10,600 \_\_\_\_? ​

If we are testing for the equality of 3 population means, we should use the _____.

MNM, Inc. has three stores located in three different areas. Random samples of the daily sales of the three stores (in $1,000s) are shown below. Store 1 Store 2 Store 3 9 10 6 8 11 7 7 10 8 8 13 11 At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores. ​