Question

A fashion designer wants to know how many new dresses women buy each year. Assume a previous study found the standard deviation to be 1.8. She thinks the mean is 5.7 dresses per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.12 at the 85% level of confidence? Round your answer up to the next integer.

Answer 1

The sample size 'n' = 242

Explanation:

Step(i):-

Given mean of the sample = 5.7

Given standard deviation of the sample (σ) = 1.8

The Margin of error (M.E) = 0.12

Level of significance = 0.85 or 85%

Step(ii):-

The margin of error is determined by

`M.E = (Z_(\alpha )S.D )/(√(n) )`

The critical value Z₀.₁₅ = 1.036

`0.12 = (1.036 X 1.8 )/(√(n) )`

Cross multiplication , we get

`√(n) = (1.036 X 1.8)/(0.12)`

√n = 15.54

Squaring on both sides, we get

n = 241.49≅ 241.5≅242

Conclusion:-

The sample size 'n' = 242