Answer:
a) Null and alternative hypothesis
b) Point estimate d = -$78
c) Test statistic t = -2.438
P-value = 0.0113
Reject H0. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that automobile insurance in Pennsylvania is significantly cheaper than the national average.
Then, the null and alternative hypothesis are:
The significance level is 0.05.
The sample has a size n=25.
The sample mean is M=1425.
A point estimate of the difference between the mean annual premium in Pennsylvania and the national mean can be calculated with the sample mean:
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=160.
The estimated standard error of the mean is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this sample size are:
This test is a left-tailed test, with 24 degrees of freedom and t=-2.438, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.0113) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that automobile insurance in Pennsylvania is significantly cheaper than the national average.
