Solution :
Given that,
Population standard deviation = = 16.5
Margin of error = E = 2
a) At 99% confidence level the z is,
= 1 - 99%
= 1 - 0.99 = 0.01
/2 = 0.005
Z/2 = 2.576
sample size = n = [Z/2* / E] 2
n = [2.576 * 16.5/ 2]2
n = 451.64
Sample size = n = 452
b) At 90% confidence level the z is,
= 1 - 90%
= 1 - 0.90 = 0.10
/2 = 0.05
Z/2 = 1.645
sample size = n = [Z/2* / E] 2
n = [1.645 * 16.5/ 2]2
n = 184.17
Sample size = n = 185
The confidence level decreases, sample size is decreases
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