Question

The mean annual premium for automobile insurance in the United States is $1,495. Being from Pennsylvania, you believe automobile insurance is cheaper there and wish to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1,439 with a standard deviation of s = $150.

If required, enter negative values as negative numbers.

a. Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.

H ₀: μ - Select your answer -greater than 1,495, greater than or equal to 1,495, equal to 1,495, less than or equal to 1,495, less than 1,495, not equal to 1,495
H _a: μ - Select your answer -greater than 1,495, greater than or equal to 1,495, equal to 1,495, less than or equal to 1,495, less than 1,495, not equal to 1,495

b. What is a point estimate of the difference between the mean annual premium in Pennsylvania and the national mean (to the nearest dollar)?
$

c. At α = .05, test for a significant difference by completing the following.

Calculate the value of the test statistic (to 2 decimals).

The p-value is - Select your answer -less than .005, between .005 and .01, between .01 and .025, between .025 and .05, between .05 and .10, between .10 and .20, greater than .20

What is your conclusion?
- Select your answer -The population mean automobile premium is higher in Pennsylvania than the national mean.The population mean automobile premium is lower in Pennsylvania than the national mean.

Answer 1

a)

null hypothesis: HO: μ		=	1495
Alternate Hypothesis: Ha: μ		<	1495

b) point estimate of the difference=1439-1495 =-56

c)

test stat t ='(x-μ)*√n/sx=

-1.87

  between .025 and .05

The population mean automobile premium is lower in Pennsylvania than the national mean