Question

1. Suppose we find that, the average engine size in our sample of size n = 30 is 192 cubic inches, with a standard deviation of 104 cubic inches. Use these statistics to compute a 90% confidence interval of population mean, that is, the average engine size for all.

Answer 1

Solution :

Given that,

sample mean = = 192

Population standard deviation =    = 104

Sample size = n =30

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2 * ( /n)

= 1.645* ( 104/  30 )

= 31.23
At 90% confidence interval
is,

- E < < + E

192 - 31.23 <   < 192 + 31.23

160.77 <   < 223.23

( 160.77 , 223.23)