Question

# The mean annual premium for automobile insurance in the United States is \$1,494. Being from Pennsylvania,...

The mean annual premium for automobile insurance in the United States is \$1,494. 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 1,494greater than or equal to 1,494equal to 1,494less than or equal to 1,494less than 1,494not equal to 1,494
H a: μ - Select your answer -greater than 1,494greater than or equal to 1,494equal to 1,494less than or equal to 1,494less than 1,494not equal to 1,494

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 .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10between .10 and .20greater 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.

#### Homework Answers

Answer #1

a)

 null hypothesis: HO: μ >= 1494 Alternate Hypothesis: Ha: μ < 1494

b)

point estimate of difference =1439-1494 = -55

c)

 standard errror of mean = sx=s/√n= 30.0000 test statistic          t              = (x-μ)*√n/sx= -1.833 p value                                 = 0.0396

p value is  between .025 and .05

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

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