Question

A sample of 16 toy dolls had a mean weight of 71.5 and a standard deviation of 12 pounds, respectively. Assuming normality, construct 95% confidence interval for the population mean weight, μ.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 71.5

sample standard deviation = s = 12

sample size = n = 16

Degrees of freedom = df = n - 1 = 16-1= 15

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,15= 2.131

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

= 2.131 * (12 / 16)

= 6.4

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

- E < < + E

71.5 - 6.4 < < 71.5 + 6.4

65.1 < < 77.9

( 65.1,77.9 ) 95% confidence interval for the population mean weight, μ is (65.1,77.9)