Exam 12: Analysis of Variance Tests

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 -Test for the main effects of factor A at the 5% significance level.

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 appropriate table value to use as the critical value at the 2.5% significance level.

Test Statistic -If we simultaneously examine the effects of two factors on the dependent variable,along with the effects of interactions between the different levels of those factors,we are performing ________________________________________.

One-way ANOVA is performed on independent samples taken from three normally distributed populations with equal variances.The following summary statistics were calculated: =6 =50 =5.2 =8 =55 =4.9 =6 =51 =5.4 The grand mean equals:

A randomized block experiment having five treatments and six blocks produced the following values: SSTR = 287, SST = 1,446, SSE = 180. The value of SSB must be:

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 error sum of squares and the error mean square.

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 test statistic.

In using the ANOVA models,the assumptions made about the data are:

Why are there more sets of null and alternative hypotheses that can be tested in two-way ANOVA compared to the one-way and the randomized block design?

What assumptions are required in using the randomized block design?

The variation that reflects the random error from the sampling process is known as 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 -Test for the interaction effects between levels of factors A and B at the 5% significance level.

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 -Test the following hypotheses at the 5% significance level: H₀ : Mean sales of shelf levels are equal H₁: Mean sales of shelf levels are not equal Test statistic = ____________________ = ____________________ Critical Value = ____________________ Conclusion: ________________________ Interpretation: ______________________________________

The variation that reflects the effect of the factor levels is known as 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. Calculate the treatment sum of squares and the treatment mean square.

Thirty finance students are randomly assigned to two different sections of a financial management class.Each section ends up consisting of 15 students.In one of the sections,computer - assisted instruction and review software is utilized; in the other section,it is not.All students are given the same final examination at the end of the semester.Does this represent a designed experiment? Explain.

What is an experiment?

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 the total sum of squares (SST)?

When there are just two treatments,the randomized block design is equivalent to the nondirectional ______________________________ t-test.

What is a factor?