Question

The sample size needed to estimate a population mean to within 50 units was found to be 97. If the population standard deviation was 250, then the confidence level used was:
a) 90%
b) 95%
c) 98%
d) 99%
e) None of the above.

Answer 1

Solution :

Given that,

standard deviation = = 250

margin of error = E = 50

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 250) / 50)²

= 97

Sample size = 97

Confidence level = 95%

Option b) is correct .