A major insuracne company is in the process of deciding whether or not to raise its base rate on automobile insurance policies. A premium analyst has determined that the base rate must be increased if the average claim amount over the past year was greater than 00. A random sample of 60 claims from last year will be collected to help make the decision.
a) Set up an appropriate one-sided hypothesis test to determine if there is sufficient evidence in the sample to conclude that the baase rate should be increased. Use a 5% level of significance and a nonstandardized test statistic. Assue that the population standard deviatino in claim amounts is 0. Stop after stating the rejection rule.
b) In business term, what is a Type II error in this situation?
c) In a random sample of 60 percent claims, the average claim amount was 42. What is the appropriate statistical decision based on your test from part ‘a’ ?
Please help IF YOU CAN !! Thank you !!
H0: Average claim over the past year did not exceed $1,400
H1: Claim exceeded $1,400
n=60 (sample size)
sigma (population SD) = 800
Rejecttion rule :
Compute z = (xbar-1400) / [800 / sqrt(60)]
xbar = mean of the sample of 60 observations .
If z > 1.64 (critical value that corresponds to 5 % level of significance for a one-tailed test), reject H0, and conclude H1.
b) Type II error : Not rejecting the hypothesis when it’s false.
That is, concluding that avergae claim fell below $1,400 when it exceeded $1,400.
c)
Sample mean 1542
Standard deviation = 800
Standard error of mean = sigma / sqrt(n)
SE = 800/7.746
Standard error of mean 103.2796
z = (xbar-mu) /se
z = (1542-1400) / 103.2796
z = 1.3749
The computed z doesn’t exceed the critical z of 1.64 at the 5 % level.
Do not reject the nul hypotheisis. The claim didn’t exceed $1,400. Base rate need not be raised.
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