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A paint manufacturer wants to determine the average drying time of a new interior wall paint....

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 (___ , ___). PLEASE SHOW ALL YOUR WORK

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Expert Solution

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)

= 5.3

The 95% confidence interval mean is,

- E < < + E

66.3-5.3 < < 66.3+5.3

61.0< < 71.6

(61 , 71.6 )

orchestra answered 2 years ago
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