Answer :
To estimate the average weekly sales of a new line of athletic footwear to within $300 with 99% confidence, the company needs to sample sales data for 87 weeks.
To estimate the average weekly sales of a new line of athletic footwear to within $300 with 99% confidence, we need to determine the sample size required. The standard deviation of the weekly sales figures is given as $1300.
To calculate the sample size, we can use the formula:
n = (z * σ / E)^2
where n is the required sample size, z is the critical value for the 99% confidence level (which is 2.576), σ is the standard deviation of the weekly sales figures, and E is the maximum allowable error or the desired margin of error (which is $300).
Substituting the given values in the formula, we get:
n = (2.576 * 1300 / 300)^2
n = 86.50
Since we cannot have a fractional number of weeks, we round up the value of n to 87. Therefore, the company needs to sample sales data for 87 weeks to estimate the average weekly sales of the new footwear to within $300 with 99% confidence.
To estimate the average weekly sales of a new line of athletic footwear to within $300 with 99% confidence, the company needs to sample sales data for 87 weeks. This can be calculated using the formula n = (z * σ / E)^2, where z is the critical value, σ is the standard deviation, and E is the maximum allowable error.
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