a A statistics practitioner would like to estimate a populat

a. A statistics practitioner would like to estimate a population mean to within 50 units with 99% confidence given that the population standard deviation is 250.What sample size should be used?

b. Redo Part a changing the standard deviation to 50.

c. Redo Part a using a 95% confidence level.

d. Redo Part a wherein we wish to estimate the population mean to within 10 units

Solution

standard deviation,sigma = 160
error,E = 40
alpha,a = 1-0.99 = 0.01

a.
Za/2 = Z0.005 = 2.575

sample size,n >= [Za/2 *(sigma/E)]^2
n >= [2.575 * (160/40)] ^2
n >= 106.09
n = 107

b.
standard deviation,sigma = 50
error,E = 40
alpha,a = 0.01
.
Za/2 = Z0.005 = 2.575
sample size,n >= [Za/2 *(sigma/E)]^2
n >= [2.575 * (50/40)] ^2
n >= 10.36
n = 11

c.
alpha,a = 1-0.95 = 0.05
Za/2 = Z0.025 = 1.96

sample size,n >= [Za/2 *(sigma/E)]^2
n >= [1.96 * (50/40)] ^2
n >= 6
n = 6

d.
error,E = 8
Za/2 = Z0.025 = 1.96

sample size,n >= [Za/2 *(sigma/E)]^2
n >= [1.96 * (50/8)] ^2
n >= 150.06
n = 151