##### Question

In: Statistics and Probability

# Construct a 95% confidence interval to estimate the population mean using the data below. What assumptions need to be made about this population?

Construct a 95% confidence interval to estimate the population mean using the data below. What assumptions need to be made about this population?

x̄ = 33 s= 9.9 n=27

The 95% confidence interval for the population mean is from a lower limit of _______  to an upper limit of _______ .

## Solutions

##### Expert Solution

= 33

s =9.9

n =27

Degrees of freedom = df = n - 1 =27 - 1 = 26

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2= 0.05 / 2 = 0.025

t /2,df = t0.025,26 = 2.056 ( using student t table)

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

= 2.056* ( 9.9/ $\sqrt$ 27)

= 3.92

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

- E < < + E

33 - 3.92 < < 33+ 3.92

29.08 < < 36.92

(lower limit= 29.08 ,upper limit= 36.92)

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