In: Statistics and Probability
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.