One of your employees has suggested that your company develop a new product. You

Question

One of your employees has suggested that your company develop a new product. You decide to take a random sample of your customers and ask whether or not there is interest in the new product. The response is on a 1 to 5scale, with 1 indicating “definitely would not purchase”; 2, “probably would not purchase”; 3, “not sure”; 4, “probably would purchase”; and 5, “definitely would purchase.” For an initial analysis, you will record the responses 1, 2, and 3 as No and 4 and5 as Yes. What sample size would you use if you wanted the 95% margin of error to be 0.15 or less?

Explanation / Answer

p = percentage picking choice =50%= 0.5(assumption)

e = margin error = 0.15

Z = z score for 95% confidence interval = 1.96

N = Population size = 100 (assumption)

X = (Z/e)2 p (1-p)

Sample size = X / [1+(X/N)]

X = (1.96/0.15)2 0.5(1-0.5)

X = 42.68

Sample size = (42.68)/[1+(42.68/100)]

Sample size = 29.91 = approximately 30

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