Question

Suppose the national average dollar amount for an automobile insurance claim is $758.83. 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 ≥ 758.83, Alternative Hypothesis: μ < 758.83. You take a random sample of claims and calculate a p-value of 0.0349 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.

A. The true average claim amount is significantly higher than $758.83.
B. The true average claim amount is higher than or equal to $758.83.
C. We did not find enough evidence to say the true average claim amount is less than $758.83.
D. The true average claim amount is significantly different from $758.83.
E. The true average claim amount is significantly less than $758.83.

Answer 1

The correct option is E

Explanation:

From the question we are told that

The population mean is
`\mu = \$ 758.83`

The null hypothesis is
`H_o : \mu \ge 758.83`

The alternative hypothesis is
`H_a : \mu < 758.83`

The p-value is
`p-value = 0.0349`

The level of significance is
`\alpha = 0.05`

Generally from the value given we see that the p-value <
`\alpha` hence

The decision rule is

Reject the null hypothesis

The conclusion is

The true average claim amount is significantly less than $758.83.