Question

Assume that you want to construct a 95% confidence interval estimate of a population mean. Find an estimate of the sample size needed to obtain the specified margin of error for the 95% confidence interval. The sample standard deviation is give. E= 20.3 cm, sample standard deviation =321.0 cm.

1201

961

916

Cannot tell from the given information

Answer 1

Solution :

Given that,

standard deviation = = 321.0 cm

margin of error = E = 20.3

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 = 1.960

Sample size = n = ((Z_/2 * ) / E)²

= ((1.960 * 321.0) / 20.3)²

= 961

Sample size = 961

Answer 961 is correct.