Exam 12: Analysis of Variance Tests

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 -State the null and alternative hypotheses. H₀: ____________________ H₁: _________________________________________

Using the randomized block design allows the reduction of the amount of error variation.

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 -Using $\alpha$ = 0.05,state the decision rule in terms of the critical value.

Test Statistic -What decisions can be made about the null hypothesis for the main effects and the interaction effects at the 0.05 significance level?

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 -State the null and alternative hypotheses to test for a difference in average number of customers per day for each store.

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 block sum of squares.

Test Statistic -A(n)____________________ variable is a variable that is observed or controlled for the purpose of determining its effect on another variable.

Test Statistic -In a two-way analysis of variance,there are "a" levels for factor A,"b" levels for factor B,and "r" replications within each of the factor-level combinations,or cells.What are the degrees of freedom for the interaction between factors A and B?

A consumer research organization is attempting to determine whether there is any difference in mpg for fully loaded 22-foot trucks leased from three companies,A-Haul,Bertz,and Glyder.Five of these trucks are rented from each company.Each truck is driven with the same weight cargo over the same 200 mile route and the mpg recorded.The results of the test are: A-Haul Bertz Glyder 3.4 5.1 7.9 4.2 2.0 8.5 5.1 8.7 5.2 4.9 6.7 8.0 3.1 6.1 8.1 Perform the hypothesis test: H₀: $\mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 }$ (Average mpg is the same for all three rental companies) H₁: Not all of the mean mpg is the same for the three companies An $\alpha$ = 0.05 is used by the consumer research organization.Is there any difference in mean mpg? Test statistic = ____________________ = ____________________ Conclusion: ____________________ Interpretation:________________________________________________________

A balanced experiment requires that:

Match each term with its definition: -Error sum of squares

Shelf Level Shelf height may affect the volume of sales for a product.In order to determine whether or not there is any effect on average sales due to product shelf height,a marketing consultant chooses four typical outlets,a supermarket,a drug store,a discount store,and a variety store,and for one week places the product chosen at one eye level.A resting week follows and the product is moved to another height and so on for three different heights.The number of units sold per week at each location and height are: Shelf Level Store Above Even Below Discount 54 55 49 Supermarket 63 60 56 Drug Store 52 52 47 Variety 44 48 41 -Compute the mean squares for treatments (MSTR).

Shelf Level Shelf height may affect the volume of sales for a product.In order to determine whether or not there is any effect on average sales due to product shelf height,a marketing consultant chooses four typical outlets,a supermarket,a drug store,a discount store,and a variety store,and for one week places the product chosen at one eye level.A resting week follows and the product is moved to another height and so on for three different heights.The number of units sold per week at each location and height are: Shelf Level Store Above Even Below Discount 54 55 49 Supermarket 63 60 56 Drug Store 52 52 47 Variety 44 48 41 -Compute the total sum of squares (SST).

Three tennis players,a beginner,an intermediate,and advanced,have been randomly selected from the membership of a racquet facility club in a large city.Using the same tennis ball,each player hits ten serves,one with each of three racquet models,with the three racquet models selected randomly.The speed of each serve is measured with a machine and the result recorded.Among the ANOVA models listed below,the most likely model to fit this situation is the:

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. State the decision rule in terms of the critical value.

Annuity A large annuity company holds many industry group stocks.Among the industries are banks,business services and construction.Seven companies from each industry group are randomly sampled to test the hypothesis that the mean price per share is the same among industries.The data are: Banks Business Services Construction =7 =7 =7 =41 =30 =24 =882 =1266 =582 -State the null and alternative hypothesis. H₀: ____________________ H₁: ___________________________________

Test Statistic -If we examine two or more independent samples to determine if their population means could be equal,we are performing ________________________________________.

Music A study to examine the effect of music type and assembly method on the productivity of workers on a production line for electronic circuit boards produced the following results: Music (B) Assembly Method (A) Classical Rock Means 1 36,32 49,47 41 2 28,32 44,40 36 Means 32 45 38.5 Overall Mean -Test for the main effects of factor A at the 5% significance level.

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. State the decision rule in terms of the critical value. What is your conclusion?

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 -Using $\alpha$ = 0.05,state the conclusion.