Question

In a random sample of 60 computers, the mean repair cost was $120 with a standard deviation of $30. Construct the 95% confidence interval for the population mean repair cost.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = $120

sample standard deviation = s = $30

sample size = n = 60

Degrees of freedom = df = n - 1 =60-1=59

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,59 = 2.001

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

= 2.001* (30 / 60)

E = 7.7

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

- E < < + E

120 - 7.7 < < 120 + 7.7

112.3 < < 127.7

(112.3,127.7) The 95% confidence interval for the population mean is ($112.3,$127.7)