Question

Anystate Auto Insurance Company took a random sample of 370 insurance claims paid out during a 1-year period. The average claim paid was $1550. Assume σ = $256.

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,

Point estimate = sample mean = = $1550

Population standard deviation = = $256

Sample size = n = 370

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 * (256 / 370)

= 21.89

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

- E < < + E

1550 - 21.89 < < 1550 + 21.89

1528.11 < < 1571.89

(1528.11 , 1571.89)

lower limit = $1528.11

upper limit = $1571.89

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 * (256 / 370)

= 34.28

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

- E < < + E

1550 - 34.28 < < 1550 + 34.28

1515.72 < < 1584.28

(1515.72 , 1584.28)

lower limit = $1515.72

upper limit = $1584.28