Sales of a new line of athletic footwear are crucial to the success of a company. The company wishes to estimate the average weekly sales of the new footwear to within $300 with 90% reliability. The initial sales indicate that the standard deviation of the weekly sales figures is approximately $1100. How many weeks of data must be sampled for the company to get the information it desires?
A) 7 weeks
B) 37 weeks
C) 23 weeks
D) 10,915 weeks

Question

Quizplus · Accepted Answer

To find the sample size (n), use the formula for the sample size of a mean: n = (Z*σ/E)^2. Here, Z is the Z-score for 90% confidence (approximately 1.645), σ is the standard deviation ($1100), and E is the margin of error ($300). Plugging in these values gives n = (1.645*1100/300)^2 ≈ 37 weeks.

Sales of a New Line of Athletic Footwear Are Crucial