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sukhopar [10]
3 years ago
10

compute an interval estimate with 90% confidence for the mean time to complete an employment test. Assuming a population standar

d deviation of three hours, what is the required sample size if the error should be less than a half hour
Mathematics
1 answer:
LuckyWell [14K]3 years ago
8 0

Answer:

<em>The required sample size 'n' = 97 .41 hours</em>

Step-by-step explanation:

<u><em>Explanation</em></u>:-

Given standard deviation of the Population 'σ' = 3 hours

Given the Margin of error = \frac{1}{2}  hour

<em>The Margin of error is determined by</em>

<em />M.E = \frac{Z_{\frac{\alpha }{2} S.D} }{\sqrt{n} }

<em>Given level of significance ∝ = 0.10 or 0.90</em>

<em>Z₀.₁₀ = 1.645</em>

<em></em>\frac{1}{2}  =\frac{1.645 X 3}{\sqrt{n} }<em></em>

<em>Cross multiplication , we get</em>

<em></em>\sqrt{n}  = 2 X 1.645 X 3<em></em>

<em>√n =  9.87</em>

<em>Squaring on both sides, we get</em>

<em>n = 97.41 hours</em>

<u><em>Final answer:</em></u><em>-</em>

<em>The required sample size 'n' = 97.41 hours</em>

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