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Exam 13: Analysis of Variance

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Question 1

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Exhibit 13.1 The following is an incomplete ANOVA table. Refer to Exhibit 13.1.For the within groups,the degrees of freedom are:

A) 6
B) 7
C) 8
D) 9

E) A) and B)
F) All of the above

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C

Question 2

Multiple Choice

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Exhibit 13.2 A researcher with Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S.cities.The underlying hypothesis is that average commute times are different across cities.To test the hypothesis,the researcher randomly selects six people from each of the four cities and records their one-way commute times to work.Refer to the below data on one-way commute time (in minutes) to work.Note that the grand mean is 36.625. Refer to Exhibit 13.2.Which of the following is the sum of squares due to treatments?

A) 5,285.83
B) 13,281.79
C) 18,567.63
D) 4,427.26

E) A) and B)
F) A) and C)

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Question 3

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The between-treatments variability is the estimate of σ² which is based on the variability due to chance.

A regional sales manager of a bank wants to know if the number of ATM transactions per day is different for four cities of equal size in the executive's region.The executive collects relevant data and obtains the following incomplete one-way ANOVA table. A)Complete the ANOVA table. B)Set up the competing hypothesis to test whether there are differences in the mean number of ATM transactions per day between the different cities. C)At the 5% significance level,what is the conclusion to the test?

Exhibit 13.9 Psychology students want to determine if there are differences between the ability of business majors and science majors to solve various types of analytic problems.They conduct an experiment and record the amount of time it takes to complete each analytic problem.The following two-way ANOVA table summarizes their findings. Refer to Exhibit 13.9.At the 5% significance level,the conclusion for the hypothesis test about the interaction term is:

Exhibit 13.8 A market researcher is studying the spending habits of people across age groups.The amount of money spent by each individual is classified by spending category (Dining out,Shopping or Electronics) and generation (Gen-X,Gen-Y,Gen-Z or Baby Boomers) .The data and an incomplete ANOVA table are shown below. Refer to Exhibit 13.8.At the 5% significance level,the critical value for the test about the interaction is:

Exhibit 13.6 A researcher wants to understand how annual mortgage payment (in dollars) depends on income level and zonal location using a two-way ANOVA without interaction.The data and an incomplete ANOVA table are shown below. Refer to Exhibit 13.6.Which of the following is the value of the test statistic for factor A?

Exhibit 13.5 A police chief wants to determine if crime rates are different for four different areas of the city (East(1) ,West(2) ,North(3) ,and South(4) sides) ,and obtains data on the number of crimes per day in each area.The one-way ANOVA table and Tukey's confidence intervals are shown below. Refer to Exhibit 13.5.The degrees of freedom for the hypothesis test are:

Exhibit 13.8 A market researcher is studying the spending habits of people across age groups.The amount of money spent by each individual is classified by spending category (Dining out,Shopping or Electronics) and generation (Gen-X,Gen-Y,Gen-Z or Baby Boomers) .The data and an incomplete ANOVA table are shown below. Refer to Exhibit 13.8.The value of MSAB is:

When two factors interact,the effect of one factor on the population mean depends upon the specific value or level present for the other factor.

One-way ANOVA analyzes the effect of one factor on the population mean and it is based on a completely randomized design.

Exhibit 13.7 A market researcher is studying the spending habits of people across age groups.The amount of money spent by each individual is classified by spending category (Dining out,Shopping or Electronics) and generation (Gen-X,Gen-Y,Gen-Z or Baby Boomers) .An incomplete ANOVA table are shown below. Refer to Exhibit 13.7.At the 5% significance level,the critical value for the hypothesis test about factor B is:

Exhibit 13.6 A researcher wants to understand how annual mortgage payment (in dollars) depends on income level and zonal location using a two-way ANOVA without interaction.The data and an incomplete ANOVA table are shown below. Refer to Exhibit 13.6.Which of the following is the value of the test statistic for factor B?

Exhibit 13.1 The following is an incomplete ANOVA table. Refer to Exhibit 13.1.At the 5% significance level,the critical value is:

If units with each block are randomly assigned to each of the treatments,then the design of the experiment is referred to as a:

Exhibit 13.8 A market researcher is studying the spending habits of people across age groups.The amount of money spent by each individual is classified by spending category (Dining out,Shopping or Electronics) and generation (Gen-X,Gen-Y,Gen-Z or Baby Boomers) .The data and an incomplete ANOVA table are shown below. Refer to Exhibit 13.8.For the interaction,the value of the test statistic is:

A golf instructor wants to determine if the drive distance is different for three golf ball brands.The instructor has several of his students drive the different brands and collects the following data. A)Construct a two-way (without interaction)ANOVA table for the data. B)At the 5% significance level,can you conclude the average drive distance differs by brand? C)Explain why the golf instructor is not interested in the hypothesis test about the golfers. D)Explain why the golf instructor uses a two-way ANOVA rather than a one-way ANOVA for brand.

A farmer plants tomato seeds into four different plots.In each plot,there is a different fertilizer treatment that is applied to the soil.After three weeks,he measures the height of each tomato plant from each of the four plots.The data he collects is given shown below. A)Construct an ANOVA table. B)Set up the competing hypothesis to test whether there are some differences in the mean heights between the different plots/fertilizers. C)At the 5% significance level,what is the conclusion to the test? D)Consider the sample standard deviations for each plot.Which of the assumptions might be violated?

Identify the assumption that is not applicable for a one-way ANOVA test.

Exhibit 13.2 A researcher with Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S.cities.The underlying hypothesis is that average commute times are different across cities.To test the hypothesis,the researcher randomly selects six people from each of the four cities and records their one-way commute times to work.Refer to the below data on one-way commute time (in minutes) to work.Note that the grand mean is 36.625. Refer to Exhibit 13.2.The competing hypotheses about the mean commute times are: