Exam 13: Experimental Design and Analysis of Variance

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.

The mean square is the sum of squares divided by _____.

Halls, 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 46 34 33 47 36 31 45 35 35 42 39 45 At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores.

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: Store 1 Store 2 Store 3 80 85 79 80 86 85 76 81 88 89 80 At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores. (Please note that the sample sizes are not equal.)

A research organization wishes to determine whether four brands of batteries for transistor radios perform equally well. Three batteries of each type were randomly selected and installed in the three test radios. The number of hours of use for each battery is given below. Brand Radio 1 2 3 4 A 25 27 20 28 29 38 24 37 21 28 16 19 Consider the three different test radios and use Excel to carry out the analysis of variance procedure for a randomized block design. Use a .05 level of significance.

Three major automobile manufacturers have entered their cars in the Indianapolis 500 race. The speeds of the tested cars are given below. Manufacturer A Manufacturer B Manufacturer C 180 177 175 175 180 176 179 167 177 176 172 190 At α = .05, test to see if there is a significant difference in the average speeds of the cars of the auto manufacturers.

The mean square is the sum of squares divided by _____.

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

Three major automobile manufacturers have entered their cars in the Indianapolis 500 race. The speeds of the tested cars are given below. Manufacturer A Manufacturer B Manufacturer C 180 177 175 175 180 176 179 167 177 176 172 190 At α = .05, test to see if there is a significant difference in the average speeds of the cars of the auto manufacturers.

To test whether the time required to fully load a standard delivery truck is the same for three work shifts (day, evening, and night), NatEx obtained the following data on the time (in minutes) needed to pack a truck. Use these data to test whether the population mean times for loading a truck differ for the three work shifts. Use α = .05. ​ Observation Day Shift Evening Shift Night Shift 1 92 83 89 2 81 93 97 3 103 79 95 4 77 102 88 5 82 84 106 Sample mean 87.0 88.2 95.0 Sample variance 110.5 85.7 52.5 ​

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

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

In the analysis of variance procedure (ANOVA), factor refers to _____.

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: Store 1 Store 2 Store 3 80 85 79 80 86 85 76 81 88 89 80 At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores. (Please note that the sample sizes are not equal.)

The ANOVA procedure is a statistical approach for determining whether the means of _____.

Eight observations were selected from each of three populations, and an analysis of variance was performed on the data. The following are the results: Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between treatments 195.58 Within treatments (Error) 10.77 Total ​ Using α = .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.

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

A dietitian wants to see if there is any difference in the effectiveness of three diets. Eighteen people, comprising a sample, were randomly assigned to the three diets. Below you are given the total amount of weight lost in a month by each person. Diet Diet B Diet C 14 12 25 18 10 32 20 22 18 12 12 14 20 16 17 18 12 14 What would you advise the dietician about the effectiveness of the three diets? Use Excel and a .05 level of significance. ​

Three different brands of tires were compared for wear characteristics. From 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 variances (both in 1,000 miles) are shown below. Brand A Brand B Brand C Average mileage 37 38 33 Sample variance 3 4 2 Using α = .05, test to see if there is a significant difference in the average mileage of the three tires. ​

The ANOVA procedure is a statistical approach for determining whether the means of _____.