Question

Use the information given to find the appropriate minimum sample size. (Round your answer up to the nearest whole number.) Estimating u correct to within 1 with probability 0.99. Prior experience suggests that the measurements will range from 16 to 40. n21

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