Question

Suppose the national average dollar amount for an automobile insurance claim is $745.88. You work for an agency in Michigan and you are interested in whether or not the state average is less than the national average. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≥ 745.88, Alternative Hypothesis: μ < 745.88. You take a random sample of claims and calculate a p-value of 0.2298 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.

Answer 1

We conclude that the state average is greater than or equal to the national average.

Explanation:

We are given that the national average dollar amount for an automobile insurance claim is $745.88. You work for an agency in Michigan and you are interested in whether or not the state average is less than the national average.

For this we are given with the hypothesis scenario as;

NULL HYPOTHESIS,
`H_0` :
`\mu \geq` $745.88 {means that the state average is greater than or equal to the national average}

ALTERNATE HYPOTHESIS,
`H_1` :
`\mu` < $745.88 { means that the state average is less than the national average}

Also, level of significance is given as 5%.

Now, we are given with the P-value of the test statistics then our decision rule is given by;

If P-value is less than the significance level, then we will reject our null hypothesis.

If P-value is more than the significance level, then we will not reject our null hypothesis.

Since, according the question;

P-value = 0.2298 or 22.98%

Level of significance = 5%

Clearly, as we can see that P-value is more than the significance level, so we have insufficient evidence to reject null hypothesis or we will accept null hypothesis.

Therefore, we conclude that the state average is greater than or equal to the national average.