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# Statistics Multiple Choice

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1. A large department store examined a sample of the 18 credit card sales and recorded the amounts charged for each of three types of credit cards: MasterCard, Visa and Discover. Six MasterCard sales, seven Visa and five Discover sales were recorded. What are the degrees of freedom for the F statistic?

A. 18 in the numerator, 3 in the denominator
B. 3 in the numerator, 18 in the denominator
C. 2 in the numerator, 15 in the denominator
D. 0 in the numerator, 15 in the denominator
E. None of the above

2. Suppose that an automobile manufacturer designed a radically new lightweight engine and wants to recommend the grade of gasoline to use. The four grades are below regular, regular, premium, and super premium. The test car made three trial runs on the test track using each of the four grades. Assuming any grade can be used at the 0.05 level, what is the critical value of F?

Kilometers per liter
Trial Below Super
Number Regular Regular Premium Premium
1 39.31 36.69 38.99 40.04
2 39.87 40.00 40.02 39.89
3 39.87 41.01 39.99 39.93

A. 1.96
B. 4.07
C. 2.33
D. 12.00
E. None of the above

3. Three different fertilizers were applied to a field of celery. In computing F, how many degrees of freedom are there in the numerator?

A. 0
B. 1
C. 2
D. 3
E. None of the above

4. Suppose a package delivery company purchased 14 trucks at the same time. Five trucks were purchased from manufacturer A, four from B and five from manufacturer C. The cost of maintaining each truck was recorded. To apply the F test, how many degrees of freedom are in the denominator?

A. 2
B. 3
C. 11
D. 14
E. None of the above

5. Several employees have submitted different methods of assembling a subassembly. Sample data for each method are:

Minutes Required for Assembly
Sample Lind's Szabo's Carl's Manley's
Number Method Method Method Method
1 16.6 22.4 31.4 18.4
2 17.0 21.5 33.4 19.6
3 16.9 22.6 30.1 17.6

How many treatments are there?

A. 3
B. 4
C. 12
D. 0
E. None of the above

6. Assume the least squares equation is Y' = 10 + 20X. What does the value of 10 in the equation indicate?

A. Y intercept
B. For each unit increased in Y, X increases by 10
C. For each unit increased in X, Y increases by 10
D. None of the above

7. What is the standard error of estimate?

A. Measure of the accuracy of the prediction
B. Based on squared vertical deviations between Y and Y'
C. Cannot be negative
D. All of the above
E. None of the above

8. What does it indicate if r = -1.00?

A. Dependent variable can be perfectly predicted by the independent variable
B. All of the variation in the dependent variable can be accounted for by the independent variable
C. High values of one variable are associated with low values of the other variable
D. Coefficient of nondetermination equals zero
E. All of the above are correct

9. What is the variable used to predict the value of another called?

A. Independent
B. Dependent
C. Correlation
D. Determination
E. None of the above

10. Which of the following statements regarding the coefficient of correlation is true?

A. It ranges from -1.0 to +1.0 inclusive
B. It measures the strength of the relationship between two variables
C. A value of 0.00 indicates two variables are not related
D. All of the above
E. None of the above

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#### Solution Preview

MULTIPLE CHOICE QUESTIONS -

1. A large department store examined a sample of the 18 credit card sales and recorded the amounts charged for each of three types of credit cards: MasterCard, Visa and Discover. Six MasterCard sales, seven Visa and five Discover sales were recorded. What are the degrees of freedom for the F statistic?
A. 18 in the numerator, 3 in the denominator
B. 3 in the numerator, 18 in the denominator
C. 2 in the numerator, 15 in the denominator
D. 0 in the numerator, 15 in the denominator
E. None of the above

You would probably use analysis of variance for this problem. A sample ANOVA table can be found here: http://www.stat.psu.edu/~resources/ClassNotes/ljs_23/sld017.htm

The total sample size would be n = 18 and the number of groups that you are comparing would be t = 3.

The F-statistic would have degrees of freedom with a numerator of t - 1 and the denominator of n - t.

Numerator
= # groups - 1
= t - 1
= 3 - 1
= 2

Denominator
= Sample size - # of groups
= n - t
= 18 - 3
= 15

2. Suppose that an automobile manufacturer designed a radically new
lightweight engine and wants to recommend the grade of gasoline to
use. The four grades are below regular, regular, premium, and super
premium. The test car made three trial runs on the test track using
each of the four grades. Assuming any grade can be used at the 0.05 level, what is the critical value of F?
...

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