Question

Imagine that you have been asked to defend to the board members of your employer your estimate of the average weekly sales potential of a new product, Widget Plus. You have test-marketed Widget Plus weekly for 36 weeks and gathered the sales data. The results were 300 units per week with a standard deviation of 60 units per week. In 400-500 words explain to the board members (as if they were college freshmen) your estimate using a confidence interval and how to properly interpret it. [Note that only the answer and not the question is included in the word count.]

Answer 1

x = 300 units per week

s = 60 units per week

n = 36 weeks

df = 36 - 1 = 35

= 0.05

The t-critical value for df = 36 - 1 = 35 and = 0.05 is 2.03.

The 95% confidence interval will be:

= x ± t-critcal*(s/√n)

= 300 ± 2.03*(60/√36)

= 279.70, 320.30

The 95% confidence interval for average weekly sales potential of a new product, Widget Plus is between 279.70 and 320.30.

We are 95% confident that the true average weekly sales potential of a new product, Widget Plus is between 279.70 and 320.30.