Question: Question 4:

Based on an analysis of U.S. vehicle registrations by Polk, a leading global market intelligence firm, the average length of ownership of vehicles that were purchased new has risen to a record of 71.4 months, or nearly six years per consumer.

A number of factors contribute to the increased length of ownership, according to Polk, which analyzed vehicle registration data between 2003 and 2011. First, consumer spending remains conservative in a weak job market with relatively high unemployment rates. Second, many buyers have longer-term financing options to secure more affordable payments. Third, vehicles produced in recent years have been more durable and more reliable than their predecessors, according to different industry reports. Several manufacturers are also offering longer warranties for new vehicles, reducing the risk for consumers who want to keep vehicles longer.

Polk's new findings, coupled with the increased average age of vehicles on the road, offer promise for the automotive aftermarket.

Based on this study, we have identified 7 Mercedes vehicles that were bought “brand new” by their owners. Between 2003 and 2011, the car owners have declared keeping their brand new cars for the following number of years before selling it. The following data shows the age of seven vehicles that were sold for the first time by their owners.

9 3 4 1 7 6 5

Let X represents the age of Mercedes cars sold for the first time by their owners.

a) Fill in the following table (show your computations in detail).

b) Would any of the ages be considered an outlier? Justify your answer.

c) Based on the above sample. Find the 95% confidence interval of the mean age of Mercedes cars sold for the first time by their owners. Interpret your results.

d) A researcher is interested in testing the following hypotheses:

H₀: The mean age of Mercedes cars sold for the first time by their owners is 5.5 years.

H₁: The mean age of Mercedes cars sold for the first time by their owners is different from 5.5 years. (claim)

i. Carry out the test using the p-value method.

ii. State your decision

iii. What does that mean? (state your conclusion)