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If X=66​, S=27​ and n=36​, and assuming that the population is normally​ distributed, construct a 95...

If X=66​, S=27​ and n=36​, and assuming that the population is normally​ distributed, construct a 95 % confidence interval estimate of the population​ mean.

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Expert Solution

Solution :

Given that,

= 66

s =27

n =36

Degrees of freedom = df = n - 1 =36 - 1 = 35

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,35 = 2.030 ( using student t table)

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

= 2.030 * (27 / 36)

= 9.1

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

- E < < + E

66-9.1   < < 66+ 9.1

56.9 < < 75.1

orchestra answered 2 years ago
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