Reference no: EM132495213

Premier Motorcars is the new Fiat dealer in Delavan, Illinois. Premier Motorcars 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 then calculates and records the miles per gallon for each purchaser. The data in Case Exhibit 21.1-1 portray the results of the tests.

Questions

a. Develop a graph of your choice that provides insight into the data.

b. Central Tendency: mean, median, mode.

c. Measures of Variability: range, variance, standard deviation.

d. Interquartile Range (IQR): compute the IQR for the sample (Q3-Q1) (do not use Excel's quartile function- it will give you the wrong answer). Then determine if there are any outliers in the data by determining the upper and lower limits which may be computed by:

i. Upper: Q3 + 1.5×IQR

ii. Lower: Q1 - 1.5×IQR

iii. This is a form of a confidence interval. Observations that are larger than the Upper or small than the Lower are sometimes considered outliers and removed from the analysis. Since the sample we have is very small, we will only identify possible outliers and retain them for all analysis procedures.

e. Conduct a hypothesis test to determine if the car in question does achieve the advertised mileage (30 miles per gallon) using 0.05 significance level.

f. Compute the proportion of purchasers with less than 30 MPG and compute the proportion of purchasers with 30 or more MPG.

g. Separate the 24 observations into two groups based on Miles per Gallon. The first group is the purchasers with less than 30 MPG, and the second group is the purchasers with 30 or more MPG.

h. Discuss any limitations you see in the results. These limitations could occur because of a weakness in the research methodology or design.