A market research firm supplies manufacturers with estimates of the retail sales

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 25 stores this year shows mean sales of 59 units of a small appliance, with a standard deviation of 7.8 units. During the same point in time last year, an SRS of 10 stores had mean sales of 51.434 units, with standard deviation 9.4 units. An increase from 51.434 to 59 is a rise of about 13%.

1. Construct a 95% confidence interval estimate of the difference 12, where 1 is the mean of this year's sales and 2 is the mean of last year's sales.

2. The margin of error is

Explanation / Answer

mu1 = 59 , s1 = 7.8 , n1 = 25 , mu2 = 51.434 , s2 = 9.4 , n2 = 10

z value at 95% CI = 1.96

1)

CI = (mu1 - mu2) + /- z * sqrt ( s1^2 / n1 + s2^2 / n2)

= ( 59 - 51.434) + / - 1.96 * sqrt ( 7.8^2 / 25 + 9.4^2 / 10)

= (0.986 ,14.145)

2) margin of error = .  z * sqrt ( s1^2 / n1 + s2^2 / n2)

= 1.96 * sqrt ( 7.8^2 / 25 + 9.4^2 / 10)

= 6.579

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