Question

1.

Anystate Auto Insurance Company took a random sample of 388 insurance claims paid out during a 1-year period. The average claim paid was $1585. Assume σ = $238.

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	$

2.The method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

1278

1257

1313

1201

1268

1316

1275

1317

1275

(a) find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)

lower limit	A.D.
upper limit	A.D.

Answer 1

Solution :

1(a) The 0.90 confidence interval for population mean is given as follows :

Where, x̄ is sample mean, σ is population standard deviation, n is sample size and Z(0.10/2) is critical z-value to construct 0.90 confidence interval.

We have, x̄ = $1585, σ = $238 and n = 388

Using Z-table we get, Z(0.10/2) = 1.6449

Hence, 0.90 confidence interval for the mean claim payment is,

The 0.90 confidence interval for the mean claim payment is ($1565.13, $1604.87).

Lower limit : $1565.13

Upper limit : $1604.87

1(b) The 0.99 confidence interval for population mean is given as follows :

Where, x̄ is sample mean, σ is population standard deviation, n is sample size and Z(0.01/2) is critical z-value to construct 0.99 confidence interval.

We have, x̄ = $1585, σ = $238 and n = 388

Using Z-table we get, Z(0.01/2) = 2.576

Hence, 0.99 confidence interval for the mean claim payment is,

The 0.99 confidence interval for the mean claim payment is ($1553.88, $1616.12).

Lower limit : $1553.88

Upper limit : $1616.12