Question

# The mean annual premium for automobile insurance in the United States is \$1,501. Being from Pennsylvania,...

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).

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

The statistical software output for this problem is:

One sample T summary hypothesis test:
μ : Mean of population
H0 : μ = 1501
HA : 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.

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