Statistics Solutions

[Solution Library] As reported by the Motor Vehicle Manufacturers Association of the United States in Motor Vehicle Facts and Figures, the number of cars

Question: As reported by the Motor Vehicle Manufacturers Association of the United States in Motor Vehicle Facts and Figures, the number of cars and trucks in the use by age are as shown in the following contingency table. Frequencies are in millions.

We are interested in testing the following null and alternative hypotheses:

From the table above we compute the table with the expected values

Expected Junior Senior Soph
F 5.2 1.6 3.2
M 7.8 2.4 4.8

The way those expected frequencies are calculated is shown below:

Finally, we use the formula to get

(fo - fe)²/fe Junior Senior Soph
F 0.0077 1.225 0.45
M 0.0051 0.8167 0.3

The calculations required are shown below:

Hence, the value of Chi-Square statistics is

The critical Chi-Square value for and degrees of freedom is . Since < , then we fail to reject the null hypothesis, which means that we don't have enough evidence to reject the null hypothesis of independence.

Age Car Truck Total
Under 6 46.2 27.8 74.0
6-8 26.9 40.0
9-11 23.3 10.7
12 & Ov er 26.8 18.6 45.4
Total 1 23.2
  1. How many cells does this contingency table have?
  2. Fill in the missing entries
  3. What is the total number of cars and trucks in use?
  4. How many vehicles are trucks?
  5. How many vehicles are between 6 and 8 years old?
  6. How many vehicles are trucks that are between 9 and 11 years old?

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Solution: The downloadable solution consists of 3 pages
Deliverable: Word Document


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