Question

A 95% confidence interval for mu using the sample results x bar = 14.0 s = 6.9 n = 30

Point Estimate ____

Margin of Error ____

The 95% Confidence interval is _____ to _____

Answer 1

Solution :

Given that,

= 14.0

s =6.9

n = 30

Degrees of freedom = df = n - 1 = 30- 1 = 29

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,29 = 2.045 ( using student t table)

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

= 2.045 * ( 6.9/ 30)

= 2.5762

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

- E < < + E

14.0 - 2.5762 < < 14.0+ 2.5762

11.4238 < < 16.5762

(11.4238 ,16.5762 )

Point Estimate __14.0__

Margin of Error ____2.5762

The 95% Confidence interval is _(11.4238 ,16.5762 )