According to ValuePenguin, the average annual cost of automobile insurance was $

Question

According to ValuePenguin, the average annual cost of automobile insurance was $1388 in the state of Nevada in 2014 (www. valuepenguin.com). An insurance broker is interested to find if the current mean annual rate of automobile insurance in Nevada is more than $1388. She took a random sample of 100 insured automobiles from the state of Nevada and found the mean annual automobile insurance rate of $1413 with a standard deviation of $122.

a. Using a 1% significance level and the critical-value approach, can you conclude that the current mean annual automobile insurance rate in Nevada is higher than $1388?

b. Find the range for the p-value for this test. What will your conclusion be using this p-value range and = .01?

Explanation / Answer

a. Here H0: mu=1388 vs H1: mu>1388

Now z statistics =xbar-mu/(sd/sqrt(n))=1413-1388/(122/10))=2.05

The z-critical value for a right-tailed test, for a significance level of=0.01 is

zc=2.33>2.05 Hence we accept the null hypothesis

b. Now p value for right tailed z test is 0.0404>0.01 Hence we accept the null hypothesis.

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