Business Smarts - Sample Module for Statistics II

Scenario I
A college senior is interested in determining the relationship between her GPA and her weekly hours of study for her prior 6 terms in college. The data on her GPAs and hours of study, in the form of (Hours of Study, GPA), are (2.8, 12), (3.0, 15), (3.0, 18), (3.1, 20), (3.5, 30), and (3.9, 42).

1) What is the sum of squares for Hours of Study?

 a)  3,757.0.

 b)  628.8.

 c)  137.0.

 d)  25.1.

 e)  None of the above.

2) What is the sum of squares for GPA?

 a)  0.828.

 b)  628.8.

 c)  0.883.

 d)  2.717.

 e)  None of the above.

3) What is the sum of squares for Hours times GPA?

 a)  463.4.

 b)  137.0.

 c)  22.717.

 d)  19.3.

 e)  None of the above.

4) What is the covariance between Hours of Study and GPA?

 a)  4.543.

 b)  2.828.

 c)  62.91.

 d)  628.8.

 e)  None of the above.

5) What is the correlation between Hours of Study and GPA?

 a)  0.005.

 b)  -0.995.

 c)  1.995.

 d)  0.995.

 e)  None of the above.

Scenario II
A human resources manager perfomed an analysis of the number of machine misfunctions and the hours of employee training as part of a workplace safety review. The data on 402 machine operators yielded the following sums of squares. The sum of squares for hours of training is 6,280. The sum of squares for the machine misfunctions is 1,060. The sum of squares for the hours of training times the machine mishaps is -1,940.

6) What is the correlation between Hours of Training and Number of Machine Misfunctions?

 a)  0.752.

 b)  -0.752.

 c)  -0.248.

 d)  -0.638.

 e)  None of the above.

7) What is the standard deviation of the correlation?

 a)  0.330.

 b)  0.752.

 c)  -0.033.

 d)  0.001.

 e)  None of the above.

8) What is the 95% confidence interval for the population correlation?

 a)  [-1.0, -0.687].

 b)  [0.687, 0.815].

 c)  [0.0, 0.687].

 d)  [-0.815, -0.687].

 e)  None of the above.

9) What is the Z-score for the population correlation for a test of H₀: ρ = 0?

 a)  -4.77.

 b)  22.8.

 c)  -22.8.

 d)  -2.8.

 e)  None of the above.

10) What is the decision and conclusion for the test of H₀: ρ = 0 in 9) with a 5% level of significance?

 a)  Reject H₀.  The hours of employee training and the number of machine
       misfunctions have an inverse linear relationship.

 b)  Reject H₀.  The hours of employee training and the number of machine
       misfunctions do not have an inverse linear relationship.

 c)  Do Not Reject H₀.  The hours of employee training and the number of machine
       misfunctions have an inverse linear relationship.

 d)  Reject H₀.  The hours of employee training and the number of machine
       misfunctions have a direct linear relationship.

 e)  None of the above.

Scenario III
The manager at an electricity power plant wants to get a better idea of how the weather affects the demand for its electricity. The data on 102 summer days yielded the following sums of squares. The sum of squares for maximum daily temperature is 10,250. The sum of squares for the daily kilowatt-hours of electricy is 7,820. The sum of squares for temperature times electricity use is 7,370.

11) What is the correlation between Maximum Daily Temperature and Total Daily Kilowatt-hours?

 a)  0.177.

 b)  0.823.

 c)  0.749.

 d)  -0.823.

 e)  None of the above.

12) What is the standard deviation of the correlation?

 a)  0.075.

 b)  0.063.

 c)  0.238.

 d)  0.057.

 e)  None of the above.

13) What is the 95% confidence interval for the population correlation?

 a)  [0.935, 0.712].

 b)  [0.572, 0.872].

 c)  [-0.712, -0.935].

 d)  [0.712, 0.935].

 e)  None of the above.

14) What is the Z-score for the population correlation for a test of H₀: ρ = 0?

 a)  14.5.

 b)  7.3.

 c)  3.1.

 d)  -14.5.

 e)  None of the above.

15) What is the decision and conclusion for the test of H₀: ρ = 0 in 14) with a 5% level of significance?

 a)  Reject H₀.  The daily maximum temperature and the number of kilowatt-hours
       of electricity used have an inverse linear relationship.

 b)  Do Not Reject H₀.  The daily maximum temperature and the number of kilowatt-hours
       of electricity used have a direct linear relationship.

 c)  Reject H_A.  The daily maximum temperature and the number of kilowatt-hours
       of electricity used have a direct linear relationship.

 d)  Reject H₀.  The daily maximum temperature and the number of kilowatt-hours
       of electricity used have a direct linear relationship.

 e)  None of the above.

Scenario IV
The claims manager at an insurance company is conducting risk analysis on the firm's automobile policies. The data on 198 policies yielded the following sums of squares on the number of miles driven per year and the number of traffic events (accidents and tickets) per year. The sum of squares for miles driven per year is 217,300. The sum of squares for the traffic events per year is 114. The sum of squares for miles driven times traffic events is 660.

16) What is the correlation between Number of Miles Driven and Number of Traffic Events?

 a)  -0.133.

 b)  0.133.

 c)  0.319.

 d)  0.033.

 e)  None of the above.

17) What is the standard deviation of the correlation?

 a)  -0.071.

 b)  0.266.

 c)  0.046.

 d)  0.071.

 e)  None of the above.

18) What is the 95% confidence interval for the population correlation?

 a)  [0.271, -0.006].

 b)  [-0.006, 0.271].

 c)  [-0.006, -0.271].

 d)  [0.006, 0.271].

 e)  None of the above.

19) What is the Z-score for the population correlation for a test of H₀: ρ = 0?

 a)  0.19.

 b)  2.78.

 c)  1.87.

 d)  -1.87.

 e)  None of the above.

20) What is the decision and conclusion for the test of H₀: ρ = 0 in 19) with a 5% level of significance?

 a)  Do Not Reject H₀.  The number of miles driven and the number of
       traffic events do not have a direct linear relationship.

 b)  Do Not Reject H₀.  The number of miles driven and the number of
       traffic events do not have an inverse linear relationship.

 c)  Do Not Reject H₀.  The number of miles driven and the number of
       traffic events do not have a direct non-linear relationship.

 d)  Reject H₀.  The number of miles driven and the number of
       traffic events have a direct linear relationship.

 e)  None of the above.

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