Question

In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From previous studies, it is assumed that the standard deviation σ is 2.4 and that the population of height measurements is normally distributed. Construct the 99% confidence interval for the population mean.

		(60.8, 65.4)
		(58.1, 67.3)
		(61.4, 65.4)
		(59.7, 66.5)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 63.4

Population standard deviation = = 2.4

Sample size = n = 10

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( /n)

= 2.576 * (2.4 / 10)

= 2.0

At 99% confidence interval estimate of the population mean is,

- E < < + E

63.4 - 2.0 < < 63.4 + 2.0

61.4 < < 65.4

(61.4 , 65.4)