Exam 13: Experimental Design and Analysis of Variance

The test scores for selected samples of sociology students who took the course from three different instructors are shown below. Instructor A Instructor B Instructor C 83 90 85 60 55 90 80 84 90 85 91 95 71 85 80 At α = .05, test to see if there is a significant difference among the averages of the three groups. ​

The critical F value with 8 numerator and 29 denominator degrees of freedom at α = .01 is _____.

Individuals were randomly assigned to three different production processes. The hourly units of production for the three processes are shown below. Production Process Process 1 Process 2 Process 3 33 33 28 30 35 36 28 30 30 29 38 34 ​ Use the analysis of variance procedure with α = .05 to determine if there is a significant difference in the mean hourly units of production for the three types of production processes.

Random samples of employees from three different departments of MNM Corporation showed the following yearly incomes (in $1,000s). Department A Department B Department C 40 46 46 37 41 40 43 43 41 41 33 48 35 41 39 38 42 45 At α = .05, test to determine if there is a significant difference among the average incomes of the employees from the three departments.

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

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.) ​

The manager of Young Corporation wants to determine whether or not the type of work schedule for her employees has any effect on their productivity. She has selected 15 production employees at random and then randomly assigned five employees to each of the three proposed work schedules. The following table shows the units of production (per week) under each of the work schedules. Work Schedule (Treatments) Work Schedule 1 Work Schedule 2 Work Schedule 3 50 60 70 60 65 75 70 66 55 40 54 40 45 57 55 At a 5% level of significance, determine if there is a significant difference in the mean weekly units of production for the three types of work schedules.

To determine whether the means of two populations are equal, _____.

An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 20 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are _____.

Random samples of employees from three different departments of MNM Corporation showed the following yearly incomes (in $1,000s). Department A Department B Department C 40 46 46 37 41 40 43 43 41 41 33 48 35 41 39 38 42 45 At α = .05, test to determine if there is a significant difference among the average incomes of the employees from the three departments.

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 design involving three treatments, the following information is provided: Treatment 1 Treatment2 Treatment 3 Sample size 5 10 5 Sample mean 4 8 9 ? The overall mean for all the treatments is ______.

An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 20 observations, were taken from the five 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 _____.

The heating bills for a selected sample of houses using various forms of heating are given below (values are in dollars). Gas-Heated Homes Central Electric Heat Pump 83 90 81 80 88 83 82 87 80 83 82 82 82 83 79 At α = .05, test to see if there is a significant difference among the average bills of the homes.

To determine whether the means of two populations are equal, _____.

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 _____.

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 Set up the ANOVA table and test for any significant main effect and any interaction effect. Use α = .05.

Samples were selected from three populations. The data obtained are shown below. Sample 1 Sample 2 Sample 3 10 16 15 13 14 15 12 13 16 13 14 14 16 10 At a 5% level of significance, use Excel to test to determine whether there is a significant difference in the means of the three populations.

In the ANOVA, treatment refers to _____.