Exam 12: Analysis of Variance Tests

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 total sum of squares (SST).

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 -Compute the mean square for the between-group variation (MSTR).

The distribution of the test statistic for analysis of variance is the:

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 -What is the computed value for Factor B (music)mean square (MSB)?

In two-way ANOVA,there are ____________________ factors,each of which operates on ____________________ or more levels.

In the randomized block design ANOVA,test units are first arranged in similar groups after the treatments are assigned.

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 treatment sum of squares (SSTR).

A university vice president for academic affairs (VPAA)collects data showing the number of papers published over the past academic year for a random sample of professors in the College of Arts and Sciences.He does the same for a random sample of 8 professors in the College of Education,and for a random sample of 10 professors in the College of Business.Does this represent a designed experiment? Explain.

Test Statistic -Compute the test statistic for the main effect for Factor B.

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. Calculate the block 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 blocks (MSB).

In the randomized block design,interaction is present when the effect of a treatment depends on the block to which it has been administered.

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 mean squares (MSE).

Lighting A study to examine the effect of lighting type and assembly method on the productivity of workers on a production line for electronic circuit boards produced the following results: Lighting (B) Assembly Method ( A ) Fluorescent Incandescent Means 1 49,32 42,45 42 2 37,30 45,32 36 Means 37 41 39 Grand Mean -What is the computed value for the sum of squares for the interaction between Factor A and Factor B (SSAB)?

In two-way ANOVA,significance tests include those for the main effects of each factor,but not for interaction effects between the combinations of factor levels.

Test Statistic -Compute the test statistic for the main effect for Factor A.

In a two-way ANOVA experiment,factor A is operating on 3 levels,factor B is operating on 4 levels,and there are 2 replications per cell.How many treatments are there in this experiment? Explain.

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 -What is the computed value for Factor B (music)sum of squares (SSB)?

How is two-way ANOVA similar to the randomized block design? How does it differ?

What is meant by a designed experiment?