Question

From a random sample of 51 adults who earn an associate’s degree from a community college (but no education beyond), the mean lifetime earnings was $1.6 million. The sample standard deviation was $0.5 million. Construct a 95% confidence interval for the mean lifetime income of adults with no more than an associate’s degree. Interpret your result.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 1.6

sample standard deviation = s = 0.5

sample size = n = 51

Degrees of freedom = df = n - 1 = 51 - 1 = 50

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,50 = 2.009

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

= 2.009 * ( 0.5 / 51 )

Margin of error = E = 0.14

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

  ± E  

= 1.6 ± 0.14

= ( 1.46, 1.74 )

We are 95% confident that the true mean lifetime income of adults with no more than an associate’s degree between 1.46 and 1.74 million