Question

In: Statistics and Probability

Construct the confidence interval for the population mean μ, if c = .95, x-bar = 11.000,...


Construct the confidence interval for the population mean μ, if c = .95,
x-bar = 11.000, s = .4, and n = 100.

Expert Solution

Solution :

Given that,

= 11.000

s =0.4

n =100

Degrees of freedom = df = n - 1 = 100- 1 = 99

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2= 0.05 / 2 = 0.025

t /2,df = t0.025,99 = 1.984 ( using student t table)

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

=1.984 * (0.4 / $\sqrt$ 100)

=0.0794

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

- E < < + E

11.000 - 0.0794 < <11.000+ 0.0794

10.9206< < 11.0794

( 10.9206, 11.0794 )

orchestra answered 2 years ago

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