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USPshnik [31]
3 years ago
10

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.
Mathematics
1 answer:
Serjik [45]3 years ago
8 0

Answer:

<em>The sample size 'n' = 242</em>

Step-by-step explanation:

<u><em>Step(i):-</em></u>

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%

<u><em>Step(ii):-</em></u>

<u><em>The margin of error is determined by</em></u>

<u><em></em></u>M.E = \frac{Z_{\alpha }S.D }{\sqrt{n} }<u><em></em></u>

The critical value Z₀.₁₅ = 1.036

0.12 = \frac{1.036 X 1.8 }{\sqrt{n} }

Cross multiplication , we get

\sqrt{n} = \frac{1.036 X 1.8}{0.12}

√n  =  15.54

Squaring on both sides, we get

n = 241.49≅ 241.5≅242

<u>Conclusion:-</u>

<em>The sample size 'n' = 242</em>

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