Exam 12: Analysis of Variance Tests

Comparing the variation between the groups to the variation within the groups is the basis of ANOVA.

A survey will be conducted to compare the United Way contributions made by sales people from three county retail corporations.Sales people are to be randomly selected from each of the three corporations and the dollar amounts of their contribution recorded.The ANOVA model most likely to fit this situation is the:

Model A consumer group is testing the gas mileage of 3 different models of cars.Several cars were driven 1000 miles and the gas mileage was recorded in the following table. Madel 1 Model 2 Madel 3 22.6 19.6 25.3 20.9 22.3 21.6 23.6 20.5 20.5 21.9 17.0 24.6 22.0 17.6 22.7 21.1 19.2 20.5 18.7 20.9 -State the null and alternative hypotheses.

Grocery store Management of the refrigerator space in a grocery store requires knowledge of the average amount of items sold.Specifically the store manager wishes to determine whether or not to allocate the same shelf space for three flavors of yogurt: raspberry,peach,and lemon.During five randomly selected weeks the sales data for each flavor were recorded.The average daily sales for each flavor were: Week Raspberry Peach Lemon 1 39 35 46 2 26 20 42 3 33 34 19 4 23 39 25 5 27 45 36 Total 148 173 168 -Calculate the test statistic. Test statistic = ____________________ = ____________________

Courses A father and his two sons played golf at four different courses with the following scores: Dad Sam Jeff Course 1 92 86 81 Course2 95 86 87 Course 3 88 81 83 Cuurse4 90 87 90 -Use a randomized block design to test for the difference of golf score means using $\alpha$ = 0.05 and using the courses as the blocking variable. What is your conclusion?

Fill in the blanks (identified by asterisks and numbers)in the following partial ANOVA table: Source of Variation SS df MS F Treatments (*1) (*2) 195 (*3) Error 625 (*4) (*5) Total 1600 25

Courses A father and his two sons played golf at four different courses with the following scores: Dad Sam Jeff Course 1 92 86 81 Course2 95 86 87 Course 3 88 81 83 Cuurse4 90 87 90 -State the null and alternative hypotheses to test for a difference in golf score means for each person.

Stores A vice president would like to know whether there is a difference between the average number of customers per day between four different stores.The following data was collected over the same 5-day period for each store. Stare 1 Stare 2 Stare 3 Stare 4 Day 1 36 12 25 30 Day 2 42 22 51 36 Day 3 39 33 40 28 Day 4 25 30 42 46 Day 5 47 34 26 35 -State the null and alternative hypotheses to test for a difference in average number of customers per day for each store.

A randomized block design ANOVA has five treatments and four blocks.The computed test statistic (value of F)is 4.35.With a 0.05 significance level,the appropriate table value and conclusion will be:

Match each term with its definition: -Sum of squares value reflecting variation between individual treatment means and the overall mean for all treatments

Grocery store Management of the refrigerator space in a grocery store requires knowledge of the average amount of items sold.Specifically the store manager wishes to determine whether or not to allocate the same shelf space for three flavors of yogurt: raspberry,peach,and lemon.During five randomly selected weeks the sales data for each flavor were recorded.The average daily sales for each flavor were: Week Raspberry Peach Lemon 1 39 35 46 2 26 20 42 3 33 34 19 4 23 39 25 5 27 45 36 Total 148 173 168 -What is the conclusion?

Stores A vice president would like to know whether there is a difference between the average number of customers per day between four different stores.The following data was collected over the same 5-day period for each store. Stare 1 Stare 2 Stare 3 Stare 4 Day 1 36 12 25 30 Day 2 42 22 51 36 Day 3 39 33 40 28 Day 4 25 30 42 46 Day 5 47 34 26 35 -Develop a randomized block design to test for the difference between the average number of customers per day between four different stores using $\alpha$ = 0.05 and using the days as the blocking variable. Calculate the treatment sum of squares and the treatment mean square.

What is the purpose of two-way ANOVA?

Grocery store Management of the refrigerator space in a grocery store requires knowledge of the average amount of items sold.Specifically the store manager wishes to determine whether or not to allocate the same shelf space for three flavors of yogurt: raspberry,peach,and lemon.During five randomly selected weeks the sales data for each flavor were recorded.The average daily sales for each flavor were: Week Raspberry Peach Lemon 1 39 35 46 2 26 20 42 3 33 34 19 4 23 39 25 5 27 45 36 Total 148 173 168 -Calculate the error mean squares (MSE).

In the randomized block design ,there is just one observation or measurement for each block-treatment combination.

In the one-way ANOVA,there is just one factor,and the null hypothesis is that the population means are equal for the respective treatments,or factor levels.Treatments are randomly assigned to the persons or test units in the experiment,so this method is also referred to as the ___________________________________ ANOVA.

Each specific level of a factor (or,in multiple-factor experiments,the interaction of a level of one factor with a level of another factor)is referred to as a(n)____________________.

Test Statistic -What is the critical F for the 0.05 level for the main effects test,Factor B?

Lawn Fertilizer To test the effectiveness of three different types of lawn fertilizer,each type was applied to six different lawns.The same size patch of lawn was mowed for all 18 test units and the grass clippings were weighed.The weight in pounds are shown in the following table. Fertilizer 1 Fertilizer 2 Fertilizer 3 Lawn 1 10.3 11.7 Lann 2 12.0 Lawn 3 9.3 10.7 Lawn 4 10.6 10.5 9.3 Lawn 5 9.1 9.8 10.4 Lawn 6 12.4 9.6 -Develop a randomized block design to test for the difference between the average number of customers per day between four different stores using $\alpha$ = 0.05 and using the days as the blocking variable. Calculate the error sum of squares and the error mean square.

In the two-way ANOVA,what is meant by the term "replications"?