Question

Anystate Auto Insurance Company took a random sample of 376 insurance claims paid out during a 1-year period. The average claim paid was $1555. Assume σ = $244.

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,

Sample size = n = 376

Z$\alpha$/2 = 1.645

Margin of error = E = Z$\alpha$/2* ($\sigma$ /$\sqrt$n)

= 1.645 * (244 / $\sqrt$ 376)

= 20.70

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

$\bar x$ - E < $\mu$ < $\bar x$ + E

1555 - 20.70 < $\mu$ < 1555 + 20.70

1534.30 < $\mu$ < 1575.70

lower limit: 1534.30

upper limit: 1575.70

Sample size = n = 376

Z$\alpha$/2 = 2.576

Margin of error = E = Z$\alpha$/2* ($\sigma$ /$\sqrt$n)

= 2.576 * (244 / $\sqrt$ 376)

= 32.41

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

$\bar x$ - E < $\mu$ < $\bar x$ + E

1555 - 32.41 < $\mu$ < 1555 + 32.41

1522.59 < $\mu$ < 1587.41

lower limit: 1522.59

upper limit: 1587.59