Chapter R, Problem 6.46RE

Dairy sales Peninsula Creameries sells both cottage cheese and ice cream. The CEO recently noticed that in months when the company sells more cottage cheese, it seems to sell more ice cream as well. Two of his aides were assigned to test whether this is true or not. The first aide’s plot and analysis of sales data for the past 12 months (in millions of pounds for cottage cheese and for ice cream) appear below.

Dependent variable is Ice cream

R-squared = 36.9%

s = 8.320 with 12 - 2 = 10 degrees of freedom

The other aide looked at the differences in sales of ice cream and cottage cheese for each month and created the following output:

Cottage Cheese	Ice Cream
Count	12
Mean	11.8000
Median	15.3500
StdDev	7.99386
IntQRange	14.3000
25th %tile	3.20000
75th %tile	17.5000

Test H₀: μ(CC - IC) = 0 vs H_a: μ(CC – IC) ≠ 0

Sample Mean = 11.800000 t-Statistic = 5.113 w>11 df

Prob = 0.0003

Lower 95% bound = 6.7209429

Upper 95% bound = 16.879057

1. a) Which analysis would you use to answer the CEO’s question? Why?
2. b) What would you tell the CEO?
3. c) Which analysis would you use to test whether the company sells more cottage cheese or ice cream in a typical year? Why?
4. d) What would you tell the CEO about this other result?
5. e) What assumptions are you making in the analysis you chose in part a? What assumptions are you making in the analysis in part c?
6. f) Next month’s cottage cheese sales are 82 million pounds. Ice cream sales are not yet available. How much ice cream do you predict Peninsula Creameries will sell?
7. g) Give a 95% confidence interval for the true slope of the regression equation of ice cream sales by cottage cheese sales.
8. h) Explain what your interval means.