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Does impulse buying really increase sales? A market researcher is curious to find out whether the location of packages of chewing gum in a grocery store really has anything to do with volume of gum sales. As a test, gum is moved to a different location in the store every Monday for four weeks (four locations). To control the experiment for type of gum, six different brands are moved around. Sales representatives keep track of how many packs of each type of gum are sold every Monday for the four weeks. The results follow. Test to determine whether there are any differences in the volume of gum sold at the various locations. Let 0.05.
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Octane An automotive engineer wanted to determine whether the octane of gasoline used in a car increases gas mileage. Recognizing that car and driver are variables that affect gas mileage, he selected six different brands of car and assigned a driver to each car, so he blocked by car type and driver. For each car (and driver), the researcher randomly selected a number from 1 to 3, with 1 representing 87-octane gasoline, 2 representing 89-octane gasoline, and 3 representing 92-octane gasoline. Then 5 gallons of the gasoline selected was placed in the car. The car was driven around a closed track at 40 miles per hour until the car ran out of gas. The number of miles driven was recorded and then divided by 5 to obtain the miles per gallon. He obtained the following results:
(a) Normal probability plots for each treatment indicate that the requirement of normality is satisfied. Verify that the requirement of equal population variances for each treatment is satisfied.
(b) Explain the role blocking plays in reducing the variability of gas mileage.
(c) Is there sufficient evidence that the mean miles per gallon are different among the three octane levels at the  level of significance?
(d) If the null hypothesis from part (c) was rejected, use Tukey’s test to determine which pairwise means differ using a familywise error rate of .
(e) Based on your results for part (d), what do you conclude?
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Open the Trust data-set
a. Consider the attributes of chicken safety (q21a to q21l) and assume they measure various dimension of safety
b. Using factor analysis and the alpha factoring method on the correlation matrix, extract the number of factors that seems most appropriate and show the scree diagram
c. Use the VARIMAX rotation and label the factors according to the factor loadings
d. Consider the table of communalities – which variable is best explained? Which one is least explained by the retained factors?
e. Draw a bar chart showing the level of the factor scores for each country
f. How do result change if maximum likelihood is chosen instead of alpha factoring?
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