Question

A paint manufacturer wants to determine the average drying time of a new interior wall paint. If for sample 12 test areas of equal size he obtained a mean drying time of 66.3 minutes and a standard deviation of 8.4 minutes, construct a 95% confidence interval for the true mean μ is (_____________ , _____________). (Show Work)

Answer 1

Solution :

Given that,

=  66.3

s =8.4

n = Degrees of freedom = df = n - 1 =12 - 1 = 11

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,11 =2.201 ( using student t table)

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

= 2.201 * (8.4/ 12)

= 5.34

The 95% confidence interval for the true mean μ is

- E < < + E

66.3 - 5.34 < < 66.3+ 5.34

60.96< < 71.64

( 60.96 , 71.64)