Question

# If X overbar =68​, S=6​, and n=81​, and assuming that the population is normally​ distributed, construct...

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.

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 = t0.025,80 = 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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