Question

A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. An SRS of  11 stores this year shows mean sales of 82 units of a small appliance, with a standard deviation of 99 units. During the same point in time last year, an SRS of 16stores had mean sales of 74.35 units, with standard deviation 10.2 units. An increase from 74.35 to 82 is a rise of about 9%.

1. Construct a 99% confidence interval estimate of the difference μ1−μ2, where μ1 is the mean of this year's sales and μ2 is the mean of last year's sales.

(a)   <(μ1−μ2)<

(b) The margin of error is _____

2. At a  0.010.01 significance level, is there sufficient evidence to show that sales this year are different from last year?

A. Yes
B. No

Answer 1

The statistical software output for this problem is:

Two sample T summary confidence interval:
μ₁ : Mean of Population 1
μ₂ : Mean of Population 2
μ₁ - μ₂ : Difference between two means
(without pooled variances)

99% confidence interval results:

Difference	Sample Diff.	Std. Err.	DF	L. Limit	U. Limit
μ1 - μ2	7.65	29.958346	10.146132	-86.99061	102.29061

Hence,

1. a) -86.99 < (μ1−μ2) < 102.29

b) Margin of error = (102.29 + 86.99)/2 = 94.64

2. No