Subaru Motors records on the entire production of 2007 Outba

Subaru Motors\' records on the entire production of 2007 Outbacks reveal that the average number of months before a major repair is normally distributed with a population mean of 60 months. Austin Subaru purchased 36 Outbacks and found that the sample\'s average months to a major repair was 64; the sample standard deviation was 5 months. Suppose you are interested whether the sample mean is different from the mean of the companys records.

4. Whats your decision at the 0.05 level of significance?

Solution

Let mu be the population mean

The test hypothesis:

Null hypothesis: mu=60

Alternative hypothesis: mu not equal to 60

The test statistic is

Z=(xbar-mu)/(s/vn)

=(64-60)/(5/sqrt(36))

=4.8

It is a two-tailed test.

Given a=0.05, the critical values are Z(0.025) = -1.96 or 1.96 (from standard normal table)

The rejection regions are if Z<-1.96 or Z>1.96, we reject the null hypothesis.

Since Z=4.8 is larger than 1.96, we reject the null hypothesis.

Answer: B. Reject H0: there are real differences between the means.