Question

1. In 2016, a small dealership leased 21 Subaru Outbacks on 2-year leases. When the cars were returned in 2018, the mileage was recorded (see below).  

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

a.       Using the 10 percent level of significance, is the dealer's mean significantly greater than the national average of 30,000 miles for 2-year leased vehicles? Follow and show the 7 steps for hypothesis testing.

b.       Determine the p-value and interpret its meaning.

c.       What assumption must you make about the population distribution in order to conduct the test in part a? Is the assumption valid? Use and include an appropriate graph from Minitab. Write a couple of sentences supporting your answer.  

d.       Verify your results (in parts a - c) using Minitab.

Answer 1

a) H0: The dealer's mean significantly not greater than the national average of 30,000 miles for 2-year leased vehicles

H1: The dealer's mean significantly greater than the national average of 30,000 miles for 2-year leased vehicles

Let the los be alpha = 5%

From the given data,

Critical t: 1.7247
Here t value < t critical value so we do not reject H0

Thus we conclude that the dealer's mean significantly not greater than the national average of 30,000 miles for 2-year leased vehicles

b)

P-Value: 0.0714

Here P-value > alpha 0.05 so we accept H0

Thus we conclude that the dealer's mean significantly not greater than the national average of 30,000 miles for 2-year leased vehicles

c) Verify the data is normal distribution or not, for that , we have to use probability plot technique in MINITAB

P-value = 0.59 which is > alpha 0.05 so we accept H0 Thus the data follows normal distribution

d) From MINITAB Output

Test Statistic t = 1.53

Here P-value > alpha 0.05 so we accept H0

Thus we conclude that the dealer's mean significantly not greater than the national average of 30,000 miles for 2-year leased vehicles