Question

Determine the sample size n needed to construct a 90?% confidence interval to estimate the population mean when

? = 48 and the margin of error equals 8.

n =

Answer 1

Solution :

Given that,

standard deviation = = 48

margin of error = E = 8

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Sample size = n = ((Z_/2 * ) / E)²

= (1.645 * 48) / 8)²

= 94.4169 = 94

Sample size = 94