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# Statistical Analysis of Quaker Oats

Quaker Oats is contemplating changing the shape of its box from the quaint cylinder presently in use. Different random samples were selected from five stores of similar size in the same region, and one of the candidate boxes was substituted for the cylinder for several days. The following results were obtained for the total number of boxes sold.

Box Shape
Store Pyramid Rectangle Cube

1 110 57 92

2 85 65 81

3 69 73 66

4 97 49 71

5 78 77 70

a. Determine the degrees of freedom for the numerator and denominator
b. Determine the critical value of the test statistic and identify the acceptance and
c. rejection regions using an alpha = .05 significance level.
d. Determine the treatments and the error sum of square. Using these values find the total sum of squares.
e. Construct the ANOVA table and compute the F value
f. Should Ho that the mean sales are identical regardless of the box shape be accepted or rejected?

#### Solution Preview

Please see the attached file for a detailed calculation and explanation.

a. Determine the degrees of freedom for the numerator and denominator
Solution:

Numerator Degree of freedom is given by (n-1), where n is the total number of treatments. Here n = 3 (pyramid, rectangle and cube). So the numerator degree of freedom is 2.

Degrees of freedom for denominator is given by (n*k-n), where k is the total number of samples in each treatment and n is the number of treatments. Therefore the denominator has the degrees of freedom as (3*5 - 3) ...

#### Solution Summary

This solution contains step-by-step calculations to determine the degrees of freedom, critical value, test statistic, error sum of square, and total sum of squares. It also provides an ANOVA table to compute the F-value to compare to the p-value to determine to either reject or accept the null hypothesis.

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