Exam 12: Analysis of Variance Tests

A randomized block design experiment produced the following data. Treatment Block 1 2 3 1 25 27 25 2 19 18 17 3 15 20 16 4 23 27 20 5 30 31 28 A)Test to determine whether the treatment means differ.(Use $\alpha$ = 0.05.) Test statistic = ____________________ = ____________________ Critical Value = ____________________ Conclusion: ____________________ Interpretation: _______________________________________ B)Test the effectiveness of the blocking variable.(Use $\alpha$ = 0.05.) Test statistic = ____________________ = ____________________ Critical Value = ____________________ Conclusion: ____________________ Interpretation: ________________________________________

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 -What is the number of the treatment degrees of freedom?

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 treatment sum of squares (SSTR).

What assumptions are required in using the two-way ANOVA?

Consider the following partial ANOVA table: Source of Variation Treatments 75 * 25 6.67 Error 60 * 3.75 Total 135 19 The numerator and denominator degrees of freedom (identified by asterisks)are,respectively,

The randomized block design with two treatments is equivalent to a non-directional:

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 error?

How does the randomized block design differ from the one-way,completely randomized design?

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 Factor A (assembly method)sum of squares (SSA)?

When there are two treatment groups,one-way ANOVA is equivalent to the pooled-variances t-test.

Which of the following statements are not true regarding the randomized block design?

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 test statistic. Test statistic = ____________________ = ____________________

The one-way ANOVA model assumes that each individual observation is considered to be the sum of the overall population mean for all the treatments plus the effect of the treatment plus

The one-way ANOVA is also referred to as the one-factor,completely randomized design,since the treatments are randomly assigned to all of the persons or other test units in the experiment.

The numerator or MSTR degrees of freedom are 4 and the denominator or MSE degrees of freedom are 20. The total number of observations in the completely randomized design must equal:

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 are the total degrees of freedom for this experiment?

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 sum of squares for blocks (SSB).

Given the significance level 0.01,the F-value for the degrees of freedom,df = (7,3)is:

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 error sum of squares (SSE)?

In the two-way ANOVA,what is meant by main effects and interactive effects?