Question

Anystate Auto Insurance Company took a random sample of 382 insurance claims paid out during a 1-year period. The average claim paid was $1520. Assume σ = $268.

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,

1)

Point estimate = sample mean = = 1520

Population standard deviation = = 268

Sample size = n = 382

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 * (268 / 382 )

= 22.56

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

- E < < + E

1520 - 22.56 < < 1520 - 22.56

1497.44 < < 1542.56

Lower limit = $1497.44

Upper limit = $1542.44

2)

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 * (268 / 382 )

= 35.32

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

- E < < + E

1520 - 35.22 < < 1520 + 35.22

1484.78 < < 1555.22

Lower limit = $1484.78

Upper limit = $1555.22