(1 point) 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 22 stores this year shows mean
sales of 85 units of a small appliance, with a standard deviation
of 11.2 units. During the same point in time last year, an SRS of
252 stores had mean sales of 74.136 units, with standard deviation
5.1units. An increase from 74.136 to 85 is a rise of about
13%.
1. Construct a 95% 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
given,
since n1 < 30, we will use t statistice to calculate the confidence interval.
The pooled estimate of standard deviation is given by,
Sp = 5.804014
Margin of error,
MOE = 1.2903
t-value at 95% is given by,
t = 1.962
Therefore,
Confidence Interval = [8.3324, 13.3955]
(a)
95% confidence interval estimate of the difference μ1−μ2 is,
8.3324 < (μ1−μ2) < 13.3955
(b)
The margin of error is,
MOE = 1.2903
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