Question

The 99% confidence interval of a population mean is (1,7). One of the following is the 95% confidence interval. Which is it?

(a) (2,6)

(b) (1,6)

(c) (0,8)

(d) (2,7)

Answer 1

mean = (1 + 7)/2 = 4

ME = 7 - 4 = 3
z-value for 99% CI is 2.5758

SE = ME/z = 3/2.5758 = 1.1647

z-value for 95% CI is 1.96
CI = (mean - z*SE, mean + z*SE)
CI = (4 - 1.96*1.1647, 4 + 1.96*1.1647)
= (1.7172, 6.2828)
Rounding
= (2, 6)

Option A