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 $500 with 90% reliability. The initial sales indicate that the standard deviation of the weekly sales figures is approximately $1200. How many weeks of data must be sampled for the company to get the information it desires?
A) 16 weeks
B) 4 weeks
C) 10 weeks
D) 7794 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, where Z is the Z-score for 90% confidence (1.645), σ is the standard deviation ($1200), and E is the margin of error ($500). Plugging in the values: n = (1.645*1200/500)^2 ≈ 15.6, which rounds up to 16 weeks.

Sales of a New Line of Athletic Footwear Are Crucial