Question

In: Statistics and Probability

Construct the confidence interval for the population mean C equals 0.95, x overbar equals 16.6 S...

Construct the confidence interval for the population mean C equals 0.95, x overbar equals 16.6

S equals 8.0, and N equals 55

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 16.6

sample standard deviation = s = 8.0

sample size = n = 55

Degrees of freedom = df = n - 1 = 55 - 1 = 54

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t_/2,df = t_0.025,54 = 2.005

Margin of error = E = t_/2,df * (s / $\sqrt$ n)

= 2.005 * (8.0 / $\sqrt$ 55)

= 2.2

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

- E < < + E

16.6 - 2.2 < < 16.6 + 2.2

14.4 < < 18.8

(14.4 , 18.8)

orchestra answered 1 year ago

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