Question

A simple random sample of size n =20 is drawn from a population that is normally distributed. The sample mean is found to be x = 61 and the sample standard deviation is found to be s =12 Construct a 95​% confidence interval about the population mean.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 61

sample standard deviation = s = 12

sample size = n = 20

Degrees of freedom = df = n - 1 = 20 - 1 = 19

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t_/2,df = t_0.025,19  = 2.093

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

= 2.093 * ( 12 / 20 )

Margin of error = E = 5.62

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

- E < < + E

61 - 5.62 < < 61 + 5.62

55.38 < < 66.62

( 55.38, 66.62 )

The 95% confidence interval estimate of the population mean is ( 55.38, 66.62 )