Question

Sales of a new line of athletic footwear are crucial to the success of a newly formed company, Fleet Shoes. Fleet wishes to estimate the average weekly sales of the new footwear within $200 with 95% reliability. The initial sales indicate the standard deviation of the weekly sales figures to be approximately $1,500. How many weeks of data must be sampled for Fleet to get the information is desires?

Answer 1

Answer:

The number of weeks required = 216 weeks

Step-by-step explanation:

Given that:

Margin of Error E = 200

Confidence interval = 95% = 0.95

Level of SIgnificance  = 1 - C.I

= 1 - 0.95

= 0.05

Standard deviation = 1500

The Critical value for Z :

$Z_{\alpha/2} =Z_{0.05/2} \\ \\ = Z_{0.025} = 1.96$

The number of weeks( i.e the sample size (n) ) required is :

$n = (\dfrac{Z_{\alpha/2} \times \sigma}{E})^2$

$n = (\dfrac{1.96 \times 1500}{200})^2$

$n = (14.7)^2$

n = 216.09

n ≅ 216 weeks