Premier Motorcars is the new fiat dealer in Delavan, Illinois, It has been regul
ID: 3216949 • Letter: P
Question
Premier Motorcars is the new fiat dealer in Delavan, Illinois, It has been regularly advertising in its local market area that the new Fiat 500 averages 30 miles to a gallon of gas and mentions that this figure may vary with driving conditions. A local consumer group wishes to verify the advertising claim. To do so, it selects a sample of recent purchasers of the Fiat 500. It asks them to drive their cars until two tanks of gasoline have been used up and to record the mileage. The group the calculates and records the miles per gallon for each purchaser. The data in Case Exhibit 21.1-1 portray the results of the tests.
Purchaser Miles per Gallon Purchaser Miler per Gallon
1 30.9 13 27.0
2 24.5 14 26.7
3 31.2 15 31.0
4 28.7 16 23.5
5 35.1 17 29.4
6 29.0 18 26.3
7 29.8 19 27.5
8 23.1 20 28.2
9 31.0 21 28.4
10 30.2 22 29.1
11 28.4 23 21.9
12 29.3 24 30.9
Questions:
1 For the sample given in the test, compute the following values:
a. Conduct a hypothesis test to determine if the car in question does achieve the advertised mileage.
b Compute the proportion of purchasers who achieved less than 30 or more MPG.
c. Conduct a hypothesis test to determine the proportion achieving less that 30 is different from the proportion achieving 30 or more MPG
Explanation / Answer
1(a) Null Hypothesis : H0 : Mileage of the care >= 30 miles
Alternative Hypothesis : Ha : Milage of the car < 30 miles
sample mean = 28.4 and standard error = 3.00
so test - statistic => t = ( 28.4 - 30.0)/ (3/sqrt(24) = -1.6/ 0.6123 = -2.61
for dF = 24- 1 = 23 and significance level alha = 0.05 tcritical= 1.714
Here t value > tcritical so we can reject the null hypothesis and can say that the company claim is incorrect and it doesn't acheive the advertised mileage.
b) Proportion of purchasers who acheived less than 30 MPG p1= 17/24 = 0.71
Proportion of purchasers who acheived morethan 30 MPG p2= 7/24 = 0.29
c) Null Hypothesis : H0 : p1 = p2
Alternative Hypothesis : Ha : p1 p2
Test statistic = ( p1 - p2) /
where = sqrt [ p( 1-p)/n] = sqrt [ 0.29 * 0.71/ 24] = 0.09
so Z = (0.71 - 0.29) / 0.092 = 4.56
for significance level 0.05 the zcritical = 1.96
so Z > zcritical so we can reject the null hypothesis and can say that the proportion acheiving less that 30 is different from the proportion acheivimg 30 or more MPG.