"Using Technology to Perform a Two-Way ANOVA Test In Exercises 15–18, use technology and the block design to perform a two-way ANOVA test. Use α=0.10. Interpret the results. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal.


[APPLET] Vehicle Sales The owner of a car dealership wants to determine whether the gender of a salesperson and the type of vehicle sold affect the number of vehicles sold in a month. The block design shows the numbers of vehicles, listed by type, sold in a month by a sample of eight salespeople.

Verified step by step guidance

1. Step 1: Organize the data into a two-way ANOVA table format, where the two factors are Gender (Male, Female) and Type of Vehicle (Car, Truck, Van/SUV). Each cell contains the sample data for the number of vehicles sold.
2. Step 2: Calculate the mean number of vehicles sold for each combination of Gender and Vehicle Type, as well as the overall mean. This helps in understanding the main effects and interaction effects.
3. Step 3: Use technology (such as statistical software or a graphing calculator) to input the data and perform the two-way ANOVA test. The software will compute the sums of squares, degrees of freedom, mean squares, F-statistics, and p-values for the main effects and interaction effect.
4. Step 4: Compare the p-values for the main effects (Gender and Vehicle Type) and the interaction effect to the significance level α = 0.10. Determine whether to reject or fail to reject the null hypotheses for each effect.
5. Step 5: Interpret the results by explaining whether Gender, Vehicle Type, or their interaction significantly affect the number of vehicles sold, based on the ANOVA test outcomes.

Key Concepts

Two-Way ANOVA

Two-Way ANOVA is a statistical method used to examine the effect of two independent categorical variables on a continuous dependent variable. It tests for main effects of each factor and their interaction effect, helping to understand if the factors independently or jointly influence the outcome.

Block Design

Block design is an experimental setup that groups subjects into blocks based on a variable to reduce variability and isolate the effect of the factors being studied. In this context, blocking by salesperson helps control for individual differences when analyzing vehicle sales.

Assumptions of ANOVA

ANOVA requires assumptions including independence of samples, normal distribution of populations, and equal population variances. These assumptions ensure the validity of the test results and accurate interpretation of the effects of the factors.