Question

A sample of 8 mountain goats has sample mean weight 85.6 lbs and sample standard deviation s=20.3 lbs. Find a 95% confidence interval for the mean weight of the population mu.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 85.6

sample standard deviation = s = 20.3

sample size = n = 8

Degrees of freedom = df = n - 1 = 8-1 =7

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,7= 2.365

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

= 2.365 * (20.3 / 8)

Margin of error = E = 17

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

- E < < + E

85.6 - 17 < < 85.6 + 17

68.6 < < 102.6

(68.6,102.6)