Question

# A market research firm supplies manufacturers with estimates of the retail sales of their products from...

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 22stores this year shows mean sales of 85 units of a small appliance, with a standard deviation of 11.2units.

During the same point in time last year, an SRS of 2525 stores had mean sales of 74.136.1 units, with standard deviation 5.1units. An increase from 74.136 to 85is a rise of about 13%.

1. Construct a 95% confidence interval estimate of the difference μ1−μ2μ1−μ2, where μ1μ1 is the mean of this year's sales and μ2μ2 is the mean of last year's sales.

2. The margin of error is

using minitab>stat>basic stta>two sample test

we have

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 22 85.0 11.2 2.4
2 25 74.14 5.10 1.0

Difference = μ (1) - μ (2)
Estimate for difference: 10.86 , Margin of Error = 5.315
95% CI for difference: (5.55, 16.18)
T-Test of difference = 0 (vs ≠): T-Value = 4.18 P-Value = 0.000 DF = 28

Ans 1 )  95% confidence interval estimate of the difference μ1−μ2 is (5.55, 16.18)

Ans 2 ) margin of error = 5.315

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