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 90% margin of error to be 0.05 or less? (Round your answer up to the nearest whole number.) participants

Question

Mathematics

Thomas Olsen

4 May, 04:10

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 90% margin of error to be 0.05 or less? (Round your answer up to the nearest whole number.) participants

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Gabriella Mcgrath · Answer 1

269

Step-by-step explanation:

The margin of Error is E = 0.05

The level of significance is, α = 1 - confidence level = 1 - 0.9 = 0.1

Assume that the proportion is, p = 0.5

From the standard normal table, observe that the critical value of Z for two tail test and 10% level of significance is 1.64

The calculation of sample size is as follows: n = (Z/E) ²p (1-p)

n = (1.64/0.05) ²0.5 (1 - 0.5)

n = (1.64/0.05) ² 0.25

n = 1075.84 * 0.25

n = 268.96 ≈ 269

The required sample size with the given margin of error approximately is 269. This value indicates the size of the customers who are using this company's products.