Answer:
(a) Null Hypothesis, :
Alternate Hypothesis, :
(b) At a .01 level of significance, we conclude that the variance in annual repair costs is larger for older automobiles.
Step-by-step explanation:
We are given that a researcher is interested in finding out whether the variance of the annual repair costs also increases with the age of the automobile.
For this, a sample of 26 automobiles 4 years old showed a sample standard deviation for annual repair costs of $170 and a sample of 25 automobiles 2 years old showed a sample standard deviation for the annual repair cost of $100.
Let the population and sample variance for 4 years old automobiles be and respectively;
And the population and sample variance for 2 years old automobiles be and respectively.
(a) Null Hypothesis, : {means that the variance in annual repair costs is same for both type of automobiles}
Alternate Hypothesis, : {means that the variance in annual repair costs is larger for older automobiles}
(b) The test statistics that will be used here is;
~ where, = 26 and = 25
Test Statistics = ~
= 2.89
Now, at 1% level of significance, F table gives the critical value of between 0.411 and 2.435 at degree of freedom 25 , 24. since our test statistics is higher than both the critical value and it will fall in rejection region so we conclude that null hypothesis will be rejected .
And we conclude that the variance in annual repair costs is larger for older automobiles.
P-value is the exact % where our test statistics lie.
If P-value > Significance level - Accept null hypothesis
If P-value < Significance level - Reject null hypothesis
So, here since our test statistics gets rejected so we conclude that p-value is less than 0.01 .