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 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."

Suppose that after reviewing the results of a previous survey, you proceeded with preliminary development of the product. Now you are at the stage where you need to decide whether or not to make a major investment to produce and market it. You will use another random sample of your customers, but now you want the margin of error to be smaller. What sample size would you use if you wanted the 95% margin of error to be 0.021 or less? (Round your answer up to the nearest whole number.)

____________ participants

Explanation / Answer

Here margin of error = critical test statistic * Standard error of the sample proportion

critical test statistic = 1.96 for (95% confidence interval)

Standard error of the sample proportion = sqrt[p* q/n]

so,

sqrt[p* q/n] * 1.96 < = 0.021

so here proportion is not given so to have minimum sample size we will assume sample proportion would be 0.5

=>

sqrt(0.5 * 0.5/n) * 1.96 < 0.021

sqrt(n/ 0.5 * 0.5) < 93.3333

n < 46.6667

n = 2177.77 or

n = 2178 should be sampled..

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.