Question

If

X overbar =68,

S=6,

and

n=81,

and assuming that the population is normally distributed, construct a

95%

confidence interval estimate of the population mean,

μ.

Answer #1

Solution :

Given that,

Point estimate = sample mean = = 68

sample standard deviation = s = 6

sample size = n = 81

Degrees of freedom = df = n - 1 = 81 - 1 = 80

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t_{
/2,df} = t_{0.025,80} = 1.990

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

= 1.990 * (6 / 81)

= 1.33

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

- E < < + E

68 - 1.33 < < 68 + 1.33

66.67 < < 69.33

(66.67 , 69.33)

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