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.
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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