Question

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?

Answer 1

Solution :

Given that,

Population standard deviation = = $ 1100

Margin of error = E = $ 300

At 90% confidence level the z is,

= 1 - 90%

= 1 - 0.90 = 0.10

/2 = 0.05

Z_/2 = Z_0.05 = 1.645

sample size = n = [Z_/2* / E] ²

n = [1.645 * 1100 / 300 ]²

n = 36.38

Sample size = n = 37 weeks.