SOLUTION: Question 10 Jennifer Cantu, Vice President of Customer Services at Tri-State Auto Insurance Inc., monitors the claims processing time of the claims division. Each week, her staff

Question 1102481: Question 10
Jennifer Cantu, Vice President of Customer Services at Tri-State Auto Insurance Inc.,
monitors the claims processing time of the claims division. Each week, her staff randomly
selects a sample of 64 claims. They test the null hypothesis that the "mean processing time
is 5 days" and the alternative hypothesis that the "mean processing time is more than 5
days" using the 0.05 level of significance. Last week the sample mean was 5.2 days.
Assuming a population standard deviation of 1.56 days, the appropriate decision is _____.
Answers:
a.
reduce the sample size
b.
do not reject the null hypothesis
c.
increase the sample size
d.
reject the null hypothesis

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
At the 0.05 level of significance,
test statistic is z=(xbar-mean)/sigma/sqrt(n)=(5.2-5)/1.56/sqrt (64)
This is z=0.2*8/1.56=1.03. This has a p-value of 0.15 which is greater than alpha of 0.05, so fail to reject Ho and b. is the answer.

If one uses a two-sided test, the 95% CI half interval is 1.96*1.56/8, z*sigma/sqrt(n), using a z test because the population sd is used. That half-interval is 0.38, so the 95% CI is [4.82, 5.58].
The appropriate decisions is b., do not reject Ho. The 95% CI contains the null hypothesis, and that means the null hypothesis is not rejected.
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