Exam 12: Analysis of Variance

Which of the following is an assumption for the one-way analysis of variance experimental design?

A large orchard owner in the state of Washington is interested in determining whether the mean number of bushels of peaches per acre is the same or different depending on the type of tree that is used. He also thinks that production may be affected by the type of fertilizer that is used. To test, he has set up a test in which a one-acre plot of peach trees with a combination each of 5 varieties and 3 fertilizer types are studied. The following data reflect the number of bushels of peaches on each acre plot. Assuming that the hypothesis tests will be conducted using an alpha equal 0.05 level, what is the value of the Fisher's LSD critical value for doing the multiple comparisons?

Explain what is meant by interaction between two factors in a two-way analysis of variance study.

In one-way analysis of variance, the within-sample variation is not affected by whether the null hypothesis is true or not.

What is meant by the term balanced design in an analysis of variance application?

Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The critical value for testing whether there is any difference among the four restaurants, using the 0.05 level of significance is approximately F = 2.8.

A test is conducted to compare three different income tax software packages to determine whether there is any difference in the average time it takes to prepare income tax returns using the three different software packages. Ten different persons' income tax returns are done by each of the three software packages and the time is recorded for each. The computer results are shown below. Based on these results and using a 0.05 level of significance which is correct regarding the primary hypothesis?

A major consumer group recently undertook a study to determine whether automobile customers would rate the quality of cars differently whether they were manufactured in the U.S., Europe, or Japan. To conduct this test, a sample of 20 individuals was asked to look at mid-range model cars made in each of the three countries. The individuals in the sample were then asked to provide a rating for each car on a scale of 1 to 1000. The following computer output resulted, and the tests were conducted using a significance level equal to 0.05. ANOVA: Two-Factor Without Replication Based upon the data, which of the following statements is true?

A company has established an experiment with its production process in which three temperature settings are used and five elapsed times are used for each setting. The company then produces one product under each and measures the resulting strength of the product. This experimental design is called a randomized complete block design.

A two-factor analysis of variance is conducted to test the effect that price and advertising have on sales of a particular brand of bottled water. Each week a combination of particular levels of price and advertising are used and the sales amount is recorded. The computer results are shown below. Based on the results above and a 0.05 level of significance, which of the following is correct?

The Tukey-Kramer method for multiple comparison is used after the analysis of variance F-test has lead us to reject the null hypothesis that all population means are equal.

Analysis of variance can only be done for fixed effects.

A real estate broker is interested in determining whether there is a difference in the mean number of days a home stays on the market before selling based on which area of the city it is located in. However, she is also concerned that the price of the house may be an issue in determining how long it takes to sell a house, so she wants to control for this. To carry out the test, she plans to randomly select one house from each part of the city in each price range. The following data show the number of days for the sample of houses selected. Using a significance level equal to 0.05, determine whether the broker was justified in controlling for house prices. Be sure to indicate what type of statistical test should be used and why.

Respond to the following questions using this partially completed one-way ANOVA table: Fill in the ANOVA table with the missing values.

In a two-factor ANOVA study, if the two factors do not interact, then neither factor A nor factor B can be considered statistically significant.

A study recently conducted by a marketing firm analyzed three different advertising designs (factor A) and four different income levels (factor B) of potential customers. At each combination of factor A and factor B, 5 customers are observed and the number of products produced is recorded. Interaction between the two factors would exist if low income customers have higher mean buying when design 1 is used, but higher income customers have higher mean buying when designs 2 and 3 are used.

In a one-way analysis of variance test, the following null and alternative hypotheses are appropriate: H0 : μ1 = μ2 = μ3 Hα : μ1 ≠ μ2 ≠ μ3

In a one-way design, which of the following is true?

In order to analyze any potential interactions between factors in an analysis of variance study, it is necessary to have at least two measurements at each level of each factor.

A start-up cell phone applications company is interested in determining whether house-hold incomes are different for subscribers to three different service providers. A random sample of 25 subscribers to each of the three service providers was taken, and the annual household income for each subscriber was recorded. The partially completed ANOVA table for the analysis is shown here: Complete the ANOVA table by filling in the missing sums of squares, the degrees of freedom for each source, the mean square, and the calculated F-test statistic.