# Will the new display with Lebron James increase soda sales by 50 cases a week?

A soda distributor claims that a new display, featuring Lebron James will increase product sales in supermarkets by an average of 50 cases in a week. For a random sample of twenty supermarkets, the average sales increase was 41.3 cases, and varied across supermarkets by about 12.2 cases.

Most imporatantly, what managerial conclusion can you draw from this data?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Null Hypothesis: Ho: M =50 cases. The average sales will increase by 50 cases a week

Alternative Hypothesis: H1: M <50. The average sales will not increase by 50 cases a week

M = 50 (hypothesized mean)

s= 12.2 (standard deviation as per the statement of the problem)

n= 20 (sample size)

sx=s/square root of n= 2.728 (standard error of the mean calculated from standard deviation and the sample size)

This is a one tailed test therefore area in one of the tails is checked

Since the sample size is less than 30 we will use t distribution

alpha (a) = 0.05 or 95% confidence interval ( area in the left tail=5%)

degrees of freedom = 20 -1 = 19

t= 1.7291 (from the tables)

Acceptance region is >M -t*sx= 45.28

Since the average sales increase is 41.3 which is less than 45.28

Do not accept the null hypothesis

The average sales increase is less than 50

At a level of significance of 5%, there is not enough evidence to support the claim that the sales increase by an average of 50 cases

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