Question

Suppose a randomly selected sample of n = 66 men has a mean foot length of x = 26.5 cm, and the standard deviation of the sample is 3 cm. Calculate an approximate 95% confidence interval for the mean foot length of men. (Round the answers to one decimal place.)

()to () cm

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 26.5

sample standard deviation = s = 3

sample size = n = 66

Degrees of freedom = df = n - 1 = 65

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,65 = 1.997

Margin of error = E = t_/2,df * (s /n)

= 1.997 * (3 / 66)

= 0.7

The 95% confidence interval estimate of the population mean is,

- E < < + E

26.5 - 0.7 < < 26.5 + 0.7

25.8 < < 27.2

(25.8 , 27.2)

Approximate 95% confidence interval for the mean foot length of men is 25.8 to 27.2 cm.