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 5 scale 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 and 5 as "Yes." What sample size would you use if you wanted the 95% margin of error to be 0.15 or less?

Answer 1

n = 43 samples

Explanation:

Error margin, E = 0.15

Confidence Interval, CI = 95% = 0.95

Significance level, α = 1 - 0.95

α = 0.05

α/2 = 0.025

To calculate population proportion, the sample size formula is:

n = 0.25 [(Zα/2) /E]²

Zα/2 = Z₀.₀₂₅ = 1.96

n = 0.25 * [(Z₀.₀₂₅)/E]²

n = 0.25 * [1.96/0.15]²

n = 42.68

n = 43 samples