Question

Use the information given to find the appropriate minimum sample size. (Round your answer up to the nearest whole number.) Es

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Answer #1

Solution :

Given that,

1) Population standard deviation = \sigma = 40 - 16 / 4 = 6 ( range rule thumb)

Margin of error = E = 1

At 99% confidence level the z is,

\alpha = 1 - 99%

\alpha = 1 - 0.99 = 0.01

\alpha/2 = 0.005

Z\alpha/2 = 2.576

sample size = n = [Z\alpha/2* \sigma / E] 2

n = [2.576 * 6 / 1]2

n = 238.88

Sample size = n = 239

n \geq 239

2) Given that,

Population standard deviation = \sigma = 7

Margin of error = E = 0.3

At 95% confidence level the z is,

\alpha = 1 - 95%

\alpha = 1 - 0.95 = 0.05

\alpha/2 = 0.025

Z\alpha/2 = 1.96

sample size = n = [Z\alpha/2* \sigma / E] 2

n = [1.96 * 7/ 0.3]2

n = 2091.53

Sample size = n = 2092

n \geq 2092

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