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 $200 with 95% reliability. The initial sales indicate that the standard deviation of the weekly sales figures is approximately $1400. How many weeks of data must be sampled for the company to get the information it desires

Answer 1

Answer:

188 weeks of data must be sampled.

Step-by-step explanation:

From the information given, we can deduce that:

The Margin of error is within = 200

The confidence interval = 95%

The level of significance = 1 - C.I

= 1 - 0.95

= 0.05

The standard deviation = 1400

The number of weeks the data must be sampled can be determined by using the formula for sample size which is:

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

$n =( \dfrac{Z_{0.05/2} \times 1400}{200} )^2$

$n =( \dfrac{1.96 \times 1400}{200} )^2$

$n =( \dfrac{2744}{200} )^2$

$n =( 13.72)^2$

n = 188.24

n ≅ 188

Thus, 188 weeks of data must be sampled.