Question

Anystate Auto Insurance Company took a random sample of 362 insurance claims paid out during a 1-year period. The average claim paid was $1505. Assume σ = $254. 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,

=1505

= 254

n = 362

a ) 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 * (254 / 362 )

= 21.96

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

- E < < + E

1505 - 21.96 < < 1505 + 21.96

1483.04 < < 1526.96

lower limit = 1483.04

upper limit = 1526.96

b ) 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 * (254 / 362 )

=34.39

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

- E < < + E

1505 - 34.39 < < 1505 + 34.39

1470.61 < < 1539.39

lower limit = 1470.61

upper limit = 1539.39