Exam 13: Experimental Design and Analysis of Variance

Three different brands of tires were compared for wear characteristics. For each brand of tire, 10 tires were randomly selected and subjected to standard wear testing procedures. The average mileage obtained for each brand of tire and sample standard deviations (both in 1000 miles) are shown below. Brand Brand Brand Average mileage 37 38 33 Sample variance 3 4 2 Use the above data and test to see if the mean mileage for all three brands of tires is the same. Let α = .05.

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.

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. ​

MNM, Inc. has three stores located in three different areas. Random samples of the sales of the three stores (in $1,000s) are shown below. Store 1 Store 2 Store 3 88 76 85 84 78 67 88 60 55 82 58 92 At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores. Show your complete work and the ANOVA table. (Please note that the sample sizes are not equal.) ​

Random samples were selected from three populations. The data obtained are shown below. Treatment 1 Treatment 2 Treatment 3 37 43 28 33 39 32 36 35 33 38 38 40 At a 5% level of significance, test to see if there is a significant difference in the means of the three populations. (Please note that the sample sizes are not equal.)

In ANOVA, which of the following is NOT affected by whether or not the population means are equal?

The number of times each experimental condition is observed in a factorial design is known as a(n) _____.

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

The F ratio in a completely randomized ANOVA is the ratio of _____.

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

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. Car A Car B Car C Average miles per gallon 42 49 44 Sample standard deviation 4 5 3 Use the above data and test to see if the mean gasoline consumption for all three models of cars is the same. Let α = .05. ​

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. ​

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 _____.

In testing for the equality of k population means, the number of treatments is _____.

MNM, Inc. has three stores located in three different areas. Random samples of the sales of the three stores (in $1,000s) are shown below. Store 1 Store 2 Store 3 88 76 85 84 78 67 88 60 55 82 58 92 At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores. Show your complete work and the ANOVA table. (Please note that the sample sizes are not equal.) ​

To test to determine whether 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: Method I Method II Method III 182 170 162 170 192 166 180 190 At the α = .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. (Please note that the sample sizes are not equal.)

The critical F value with 6 numerator and 60 denominator degrees of freedom at α = .05 is _____.

A term that means the same as the term "variable" in an ANOVA procedure is _____.

Three different brands of tires were compared for wear characteristics. For each brand of tire, 10 tires were randomly selected and subjected to standard wear testing procedures. The average mileage obtained for each brand of tire and sample standard deviations (both in 1000 miles) are shown below. Brand Brand Brand Average mileage 37 38 33 Sample variance 3 4 2 Use the above data and test to see if the mean mileage for all three brands of tires is the same. Let α = .05.

The F ratio in a completely randomized ANOVA is the ratio of _____.