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

We need to sample at least 37 weeks of data.

Step-by-step explanation:

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

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

So it is z with a pvalue of , so

Now, find the margin of error M as such

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

So

Rounding up

We need to sample at least 37 weeks of data.

2

step-by-step explanation:

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