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how many weeks of data must be randomly sampled to estimate the mean weekly sales of a new line of athletic footwear? We want 98% confidence that the sample mean is within $500 of the population mean, and the population standard deviation is known to be $1300

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2 votes

Answer:

We need to sample at least 37 weeks of data.

Explanation:

We have that to find our
\alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:


\alpha = (1-0.98)/(2) = 0.01

Now, we have to find z in the Ztable as such z has a pvalue of
1-\alpha.

So it is z with a pvalue of
1-0.01 = 0.99, so
z = 2.327

Now, find the margin of error M as such


M = z*(\sigma)/(√(n))

We want 98% confidence that the sample mean is within $500 of the population mean, and the population standard deviation is known to be $1300

This is at least n weeks, in which n is found when
M = 500, \sigma = 1300

So


M = z*(\sigma)/(√(n))


500 = 2.327*(1300)/(√(n))


500√(n) = 2.327*1300


√(n) = (2.327*1300)/(500)


(√(n))^(2) = ((2.327*1300)/(500))^(2)


n = 36.6

Rounding up

We need to sample at least 37 weeks of data.

User Sanek Zhitnik
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