Exam 16: More on Analysis of Variance

A marketing researcher was studying the effect of a supermarket display on sales of a new product. There were two designs for the display: the first had greater visual appeal and the second contained more factual information about the product. Each type of display could be made in three sizes: small, medium, or large. Eighteen supermarkets were available for the study, and three supermarkets were selected at random to display each combination of design and size. The number of units of the product sold over a two-week period was recorded for each supermarket. For the resulting data, a two-way ANOVA was run, with the partial ANOVA table given below. Analysis of variance for sales: In the ANOVA table, the test for the main effect of design has a P-value of 0.613, which indicates that:

A researcher wished to compare the effect of the frequency of the rate of stepping on heart rate in a step-aerobics workout. A collection of 30 adult volunteers, 15 women and 15 men, was selected from a local gym. The men were randomly divided into three groups of five subjects each. Each group did a standard step-aerobics workout, with group 1 at a low rate of stepping, group 2 at a medium rate of stepping, and group 3 at a rapid rate. The women were also randomly divided into three groups of five subjects each. As with the men, each group did one of the three standard step-aerobics workouts. The mean heart rate at the end of the workout for all subjects was determined (in beats per minute). A partial ANOVA table for these data is given below. Analysis of variance for heart rate: The plots and the P-value for the test for interaction show little evidence of interaction, which means that:

A marketing researcher was studying the effect of a supermarket display on sales of a new product. There were two designs for the display: the first had greater visual appeal and the second contained more factual information about the product. Each type of display could be made in three sizes: small, medium, or large. Eighteen supermarkets were available for the study, and three supermarkets were selected at random to display each combination of design and size. The number of units of the product sold over a two-week period was recorded for each supermarket. For the resulting data, a two-way ANOVA was run, with the partial ANOVA table given below. Analysis of variance for sales: Which statement best describes the type of experiment being run?

A marketing researcher was studying the effect of a supermarket display on sales of a new product. There were two designs for the display: the first had greater visual appeal and the second contained more factual information about the product. Each type of display could be made in three sizes: small, medium, or large. Eighteen supermarkets were available for the study, and three supermarkets were selected at random to display each combination of design and size. The number of units of the product sold over a two-week period was recorded for each supermarket. For the resulting data, a two-way ANOVA was run, with the partial ANOVA table given below. Analysis of variance for sales: The numerical value of the F statistic used for testing for the main effect of size is:

A population of flights can be classified according to two factors: duration (short, medium, or long) and purpose (vacation or business). We are interested in whether either of these factors has an effect on price. The table below gives mean prices for a balanced population. A medium-distance business flight costs $300 more than a short-distance business flight. However, a medium-distance vacation flights is only $200 more than a short-distance vacation flight. This difference between business and vacation flights is called:

A researcher wished to compare the effect of the frequency of the rate of stepping on heart rate in a step-aerobics workout. A collection of 30 adult volunteers, 15 women and 15 men, was selected from a local gym. The men were randomly divided into three groups of five subjects each. Each group did a standard step-aerobics workout, with group 1 at a low rate of stepping, group 2 at a medium rate of stepping, and group 3 at a rapid rate. The women were also randomly divided into three groups of five subjects each. As with the men, each group did one of the three standard step-aerobics workouts. The mean heart rate at the end of the workout for all subjects was determined (in beats per minute). A partial ANOVA table for these data is given below. Analysis of variance for heart rate: Since there is little evidence of interaction and the main effect of stepping is significant, we can conclude that:

A study compared dry matter intake (dmi) in mature cows (C) and heifers (H) receiving no treatment (control), treatment A, or treatment B. The two factors are type of animal and treatment. Each factor combination has eight animals. The above plot of the means, which is derived from a two-factor analysis of variance, is called:

A population of flights can be classified according to two factors: duration (short, medium, or long) and purpose (vacation or business). We are interested in whether either of these factors has an effect on price. The table below gives mean prices for a balanced population. The average price for short flights is:

Instructors gave caffeine to fruit flies to see if it affected their rest. The three treatments were a control, a low caffeine dose of 1 mg/ml of blood, and a higher caffeine dose of 5 mg/ml of blood. Fifteen fruit flies were assigned at random to three treatments, five to each treatment. The minutes of rest measured over a 12-hour period were recorded; the data follow. Minitab was used to obtain 95% simultaneous confidence intervals for the differences in means among the three treatments using Tukey's procedure; the results follow. The average minutes of rest for the five fruit flies assigned to the low-dose group was:

A study compared dry matter intake (dmi) in mature cows (C) and heifers (H) receiving no treatment (control), treatment A, or treatment B. The two factors are type of animal and treatment. Each factor combination had eight animals. A partial ANOVA table is given below. The F test for interaction is:

Instructors gave caffeine to fruit flies to see if it affected their rest. The three treatments were a control, a low caffeine dose of 1 mg/ml of blood, and a higher caffeine dose of 5 mg/ml of blood. Fifteen fruit flies were assigned at random to three treatments, five to each treatment. The minutes of rest measured over a 12-hour period were recorded; the data follow. Minitab was used to obtain 95% simultaneous confidence intervals for the differences in means among the three treatments using Tukey's procedure; the results follow. From these intervals:

Which test should be used to determine whether there are differences between the means of several groups that cannot be segmented according to two different explanatory variables?

A marketing manager studied the effect of packaging on sales. Four designs were chosen: design 1 had three colors, design 2 had three colors and cartoons, design 3 had five colors, and design 4 had five colors and cartoons. The ANOVA table below analyzes the effects of varying the number of colors and adding cartoons on sales. This is an example of a two-factor factorial design. Analysis of Variance for Sales The estimate of the standard deviation  is given by:

A population of flights can be classified according to two factors: duration (short, medium, or long) and purpose (vacation or business). We are interested in whether either of these factors has an effect on price. The table below gives mean prices for a balanced population. The difference between the cost of a business flight and the cost of a vacation flight:

A marketing researcher was studying the effect of a supermarket display on sales of a new product. There were two designs for the display: the first had greater visual appeal and the second contained more factual information about the product. Each type of display could be made in three sizes: small, medium, or large. Eighteen supermarkets were available for the study, and three supermarkets were selected at random to display each combination of design and size. The number of units of the product sold over a two-week period was recorded for each supermarket. For the resulting data, a two-way ANOVA was run, with the partial ANOVA table given below. Analysis of variance for sales: What conclusion should be drawn from this test?

Which test should be used to determine whether there are differences between the means of several groups that can be segmented according to two different explanatory variables?

A marketing manager studied the effect of packaging on sales. Four designs were chosen: design 1 had three colors, design 2 had three colors and cartoons, design 3 had five colors, and design 4 had five colors and cartoons. The plot below provides means at all four levels of color and cartoon combinations. Based on the plot, what can we conclude?

A population of flights can be classified according to two factors: duration (short, medium, or long) and purpose (vacation or business). We are interested in whether either of these factors has an effect on price. The table below gives mean prices for a balanced population. The average cost of a business flight is:

A marketing manager studied the effect of packaging on sales. Four designs were chosen: design 1 three colors, design 2 had three colors and cartoons, design 3 had five colors, and design 4 had five colors and cartoons. The ANOVA table below analyzes the effects of varying the number of colors and adding cartoons on sales. There were 20 stores where the boxes with the new designs were sold. Analysis of Variance for Sales The F statistic for testing that there is no interaction is:

A population of flights can be classified according to two factors: duration (short, medium, or long) and purpose (vacation or business). We are interested in whether either of these factors has an effect on price. The table below gives mean prices for a balanced population and shows the presence of interactions. If a study is conducted and we think there may be interactions, we should: