Question

The mean annual premium for automobile insurance in the United States is $1,501. 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 $1,442 with a standard deviation of s= $155.

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 1,501), (greater than or equal to 1,501), (equal to 1,501), (less than or equal to 1,501), (less than 1,501), (not equal to 1,501)
H a: μ - Select your answer: (greater than 1,501), (greater than or equal to 1,501), (equal to 1,501), (less than or equal to 1,501), (less than 1,501), (not equal to 1,501)

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 -

1. The population mean automobile premium is higher in Pennsylvania than the national mean)

2. The population mean automobile premium is lower in Pennsylvania than the national mean.Item 6

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test:
μ : Mean of population
H₀ : μ = 1501
H_A : μ < 1501

Hypothesis test results:

Mean	Sample Mean	Std. Err.	DF	T-Stat	P-value
μ	1442	31	24	-1.9032258	0.0345

Hence,

a) Ho: μ greater than or equal to 1,501

Ha: μ less than 1501

b) Point estimate of difference = 1442 - 1501 = -59

c) Test statistic = -1.90

p - Value is between 0.025 and 0.05

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