Question

An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,800. They are concerned that the true mean is actually higher than this because they could potentially lose a lot of money. They randomly select 40 claims and calculate a sample mean of $1,950. Assuming that the standard deviation of claims is $500, and set ® = :05, test to see if the insurance company should be concerned. Determine the critical value, test statistic, and decision.

The critical value, test statistic, and decision are

Answer 1

H0: $\mu$ = 1800

Ha: $\mu$ > 1800

Test statistics

z = ($\bar{x}$ - $\mu$ ) / ($\sigma$ / sqrt(n) )

= ( 1950 - 1800) / (500 / sqrt(40) )

= 1.90

Critical value at 0.05 significance level = 1.645

Since test statistics > 1.645, Reject H0.

We conclude that we have sufficient evidence to support the claim that the true mean is actually higher than $1800.