Exam 12: Analysis of Variance Tests

The starting point for ANOVA is often an experiment in which the goal is to determine whether various levels of an independent variable,or factor,might be exerting different effects on the dependent variable,or measurement.When there is only one factor in an experiment,each factor level can be referred to as a ____________________.

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

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 number of the error degrees of freedom?

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 total degrees of freedom?

Alumni clubs Three alumni clubs for a university have members who contribute to the university athletic program.The amount of contribution (in dollars)for six contributors randomly selected from each city to test the hypothesis that the mean contribution is the same among alumni clubs is given below,followed by the total for each city: Banks Business Services Construction =7 =7 =7 =41 =30 =24 =882 =1266 =582 -Calculate the error mean squares (MSE).

Alumni clubs Three alumni clubs for a university have members who contribute to the university athletic program.The amount of contribution (in dollars)for six contributors randomly selected from each city to test the hypothesis that the mean contribution is the same among alumni clubs is given below,followed by the total for each city: Banks Business Services Construction =7 =7 =7 =41 =30 =24 =882 =1266 =582 -Calculate the error sum of squares (SSE).

One-way ANOVA is performed on three independent samples with n₁ = 6,n₂ = 7,and n₃ = 8.The critical value obtained from the F-table for this test at the 2.5% level of significance equals:

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 number of the treatment degrees of freedom?

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 error sum of squares and the error mean square.

A study will be undertaken to examine the effect of two kinds of background music and of two assembly methods on the output of workers at a fitness shoe factory.Two workers will be randomly assigned to each of four groups,for a total of eight in the study.Each worker will be given a headphone set so that the music type can be controlled.The number of shoes completed by each worker will be recorded.Does the kind of music or the assembly method or a combination of music and method affect output? The ANOVA model most likely to fit this situation is the one-way analysis of variance.

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 error sum of squares (SSE).

The calculated value of F in a one-way analysis is 8.23.The numerator degrees of freedom and denominator degrees of freedom are 4 and 8,respectively.The most accurate statement to be made about the p-value is:

Test Statistic -Compute the test statistic for the interaction effect between Factor A and Factor B.