Question

Construct a 90% confidence interval to estimate the population mean using the data below

sample mean x = 70

o = 10

n = 30

N = 300

The 90% confidence interval for the populatin mean is ( __ , ___ )

Answer 1

From the given information, x = 70,0 = 10, N = 300 and n = 30. The objective is to construct a 90% confidence interval to estimate the population mean. The level of significance is, 1-a=0.90 a=1-0.90 a=0.10 Compute the 90% confidence interval. lo N-n CI = I 2 /2 (finite population correction factor) T N -1 -70+1 645 10 300–30 (Use the Excel function NORMSINV(0.10/2)) = 70 71.04s ( 130 V 300-1 (Use the Exc =( 70-2.8540,70+2.8540) =(67.146, 72.854) (67.15, 72.85) Therefore, the 90% confidence interval for the population mean is (67.15, 72.85).