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 $1540. Assume σ = $234.

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 = 358

Z/2 = 1.645

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

= 1.645 * ( 234 / 358)

Margin of error = E = 20.34

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

- E < < + E

1540 - 20.34 < < 1540 + 20.34

1519.66 < < 1560.34

lower limit: $1591.66

upper limit: $1560.34

Sample size = n = 358

Z/2 = 2.576

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

= 2.576 * ( 234/ 358)

Margin of error = E = 31.86

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

- E < < + E

1540 - 31.86 < < 1540 + 31.86

1508.14 < < 1571.86

lower limit: $1508.14

upper limit: $1571.86