Question

A random sample of 225 accident victims from a 5 year period were selected and the victims who suffered a fatality were recorded. The results were that x-bar was 11.6 and s = 4.1 fatalities. Estimate the mean number of fatalities over the 5 year period with 90% confidence.

Answer 1

Given that,

= 11.6

s =4.1

n =225

Degrees of freedom = df = n - 1 =225 - 1 = 224

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,224 = 1.652    ( using student t table)

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

=1.652 * (4.1 / 225)

E= 0.4516

The 90% confidence interval estimate of the population mean is,

- E < < + E

11.6 - 0.4516 < <11.6 + 0.4516

11.1484< < 12.0516

( 11.1484, 12.0516 )