Question

Find the 95% confidence interval for the mean number of times people itch themselves per hour (iph), given that a sample of 20 people had a mean rate of 1.3 iph with a standard deviation of 0.5 iph. Assume an unknown σ and a close to normally distributed population.

Answer 1

solution

Given that,

= 1.3

s =0.5

n = 20

Degrees of freedom = df = n - 1 = 20- 1 =19

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,19 = 2.093 ( using student t table)

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

= 2.093 * ( 0.5/ 20) = 0.2340

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

- E < < + E

1.3 -0.2340 < < 1.3+ 0.2340

1.0660< < 1.5340

( 1.0660, 1.5340 )