Question

If n = 5 , x(bar) =31, and s = 8, construct a confidence interval at a 80% confidence level. Give your answers to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 31

sample standard deviation = s = 8

sample size = n = 5

Degrees of freedom = df = n - 1 = 5-1= 4

At 80% confidence level the t is ,

= 1 - 80% = 1 - 0.8 = 0.2

/ 2 = 0.2 / 2 = 0.1

t /2,df = t0.1,4 = 1.533

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

= 1.533* (8 / 5)

E = 5.5

The 80% confidence interval estimate of the population mean is,

- E < < + E

31 - 5.5 < < 31 + 5.5

25.5 < < 36.5

(25.5,36.5)