Question

In: Statistics and Probability

Make a 99% confidence interval for u if: mean= 38.54 s=3.75 n=36

Make a 99% confidence interval for u if:
mean= 38.54
s=3.75
n=36

Expert Solution

Solution :

Given that,

sample mean = = 38.54

sample standard deviation = s = 3.75

sample size = n = 36

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

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t_/2,df = t_0.005,35 = 2.724

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

= 2.724 * ( 3.75 / $\sqrt$ 36 )

= 1.70

The 99% confidence interval estimate of the population mean is,

- E < < + E

38.54 - 1.70 < < 38.54 + 1.70

36.84 < < 40.24

( 36.24 , 40.24 )

orchestra answered 2 years ago

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