Question

Anystate Auto Insurance Company took a random sample of 358 insurance claims paid out during a 1-year period. The average claim paid was $1530. Assume σ = $230.

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,

= $1530

= $230

n = 358

a) At 0.90 confidence level the z is,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1/ 2 = 0.05

Z_/2 = Z_0.05 =1.645

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

= 1.645 * (230 / 358)

= 20

At 0.90 confidence interval estimate of the population mean is,

- E < < + E

1530 - 20 < < 1530 + 20

1510 < < 1550

(1510, 1550)

Lower limit = $1510

Upper limit = $1550

b) At 0.99 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 * (230 / 358)

= 31.31

At 0.99 confidence interval estimate of the population mean is,

- E < < + E

1530 - 31.31 < < 1530 + 31.31

1498.69 < < 1561.31

(1498.69, 1561.31)

Lower limit = $1498.69

Upper limit = $1561.31

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