Question

Anystate Auto Insurance Company took a random sample of 368 insurance claims paid out during a 1-year period. The average claim paid was $1595. Assume σ = $266.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Answer 1

Solution :

Given that,

= $1595

=$266

n = 386

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645* (266/ 368)

= 22.81

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

- E < < + E

1595 - 22.81 < < 1595 + 22.81

1572.19< < 1617.81

(1572.19,1617.81 )

lower limit = $1572.19

upper limit = $1617.81

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576* (266 / 368)

= 35.72

At 99% confidence interval estimate of the population mean is,

- E < < + E

1595 - 35.72 < < 1595 + 35.72

1559.28< < 1630.72

(1559.28,1630.72 )

lower limit = $1559.28

upper limit = $1630.72