Question

Anystate Auto Insurance Company took a random sample of 380 insurance claims paid out during a 1-year period. The average claim paid was $1580. 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,

Point estimate = sample mean = = $ 1580

Population standard deviation =    = $ 268

Sample size = n = 380

a) At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645 * ( 268 /  380 )

= 22.62

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

  ± E

$ 1580 ± 22.62

( $ 1557.38, $ 1602.62 )

lower limit = $ 1557.38

upper limit = $ 1602.62

b) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

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

= 1.96 * ( 268 /  380 )

= 26.95

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

  ± E

$ 1580 ± 26.95

( $ 1553.05, $ 1606.95 )

lower limit = $ 1553.05

upper limit = $ 1606.95