In 2008, a small dealership leased 21 Suburu Outbacks on 2-year leases. When the

Question

In 2008, a small dealership leased 21 Suburu Outbacks on 2-year leases. When the cars were returned in 2010, the mileage was recorded (see below).
1. Find the sample mean with 90% confidence interval.

2. Is the dealer's mean significantly greater than the national average of 30,000 miles for 2-year leased vehicles, using the 5 percent level of significance?
Find answer using the following steps :

Step 1: State the Hypotheses
Step 2: Specify the Decision Rule
Step 3: Calculate the Test Statistic
Step 4: Make the Decision
Calculate p-value also and give interpretations.

Data:
40,060   24,960   14,310   17,370   44,740   44,550   20,250
33,380   24,270   41,740   58,630   35,830   25,750   28,910
25,090   43,380   23,940   43,510   53,680   31,810   36,780

Explanation / Answer

1. The 90% c.i=xbar+-t20,0.10SE(xbar)

=33949.52+-1.725(11866.17/sqrt 21)

=29483 to 38416

2. H0:mu=30,000

H1:mu>30,000

Reject H0, if t>1.725

t=(xbar-mu)/(s/sqrt n)

=(33950-30000)/(11866/sqrt 21)

=1.53

The test statistic do not fall in critical region. fAil to reject H0. Insufficient sample evidence to cocnclude that dealer's mean significantly greater than national average.

p value is 0.0708. p value is not less than alpha=0.05. Result is insignificant at alpha=0.05.

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