Question

1. A random sample of 90 full-size trucks had a mean weight of 7,785 pounds and a standard deviation of 845.6 pounds. Construct a 95% confidence interval for the population mean (4 Points).

Conditions:

Work:

Interval:

Conclusion:

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 7785

Population standard deviation =     = 845.6

Sample size n =90

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z / 2   = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96* ( 845.6 / 90 )

= 174.7028
At 95% confidence interval estimate of the population mean
is,

- E <   < + E

7785 - 174.7028 <   < 7785+ 174.7028

7610.2972 <   < 7959.7028

( 7610.2972 , 7959.7028 )