BA 275 Quizzes

Winter 2007

Quiz #7

Name (please print) / Answer Key
Section (circle one) / 12noon – 1:50pm / 2:00 – 3:50pm / 4:00 – 5:50pm

Part I. Has the number of home runs hit by major league teams been changing over time? For the 41 years from 1960 to 2000, the average number of home runs hit per game per team for each season was computed in order to assess any change over time. In addition to the use of year to predict the average number of home runs per game per team in that year, it was pointed out that after the 1976 season the manufacturer of major league baseballs was changed from Spaulding to Rawlings. Therefore, a dummy variable (an indicator) was also included. A multiple regression analysis was performed using the following model.

,

where Y = home runs per game per team, X1 = Year (e.g., 1960, 1961, … etc.), and X2 = 0 if the Spaulding baseball was used; and = 1 if the Rawlings baseball was used. The regression results were obtained.

Standard / T
Parameter / Estimate / Error / Statistic / P-Value
CONSTANT / -27.91180 / 12.8900 / -2.16538 / 0.036702
Year / 0.014977 / 0.00650 / 2.304154 / 0.026775
Baseball Manufacturer / -0.107816 / 0.11573 / ? / ?

Analysis of Variance

Source / Sum of Squares / Df / Mean Square / F-Ratio / P-Value
Model / 0.744384 / 2 / 0.37219 / 5.569696
Residual / 2.539330 / 38 / 0.066824
Total (Corr.) / ? / 40

1.  By using the regression results above, what would be the predicted average number of home runs per game per team in 1998? A point estimate is sufficient.

-27.91180 + 0.014977 (1998) – 0.107816 (1) = 1.90443

2.  Calculate the value of R-squared.

SStotal = SSmodel + SSresidual = 0.744384 + 2.539330 = 3.283714.
R-squared = SSmodel / SStotal = 0.744384 / 3.283714 = 0.22669.

3.  Construct a 99% confidence interval for b1, the coefficient of the variable Year. Write your answer in the following format for full credit: ( point estimate ) ± ( margin of error ).

( 0.014977 ) ± ( 2.750 ´ 0.00650 )
The degrees of freedom is n – p – 1 = 41 – 2 – 1 = 38

4.  Did the change in manufacturer have any effect on the average number of home runs hit per game per team? To answer this question, what would be the appropriate null and alternative hypotheses?

Null hypothesis (H0) / b2 = 0
Alternative hypothesis (Ha) / b2 ≠ 0

5.  Based on the regression results, the p-value for the test in Part I – Question 4 is

A)  greater than 0.05.

B)  between 0.05 and 0.01.

C)  between 0.01 and 0.005.

D)  below 0.005.

The “evidence” b2 = –0.107816 has a t statistic –0.93162, less than one standard deviation below the null hypothesis: b2 = 0. Hence, the p-value is greater than 0.05. Answer: A.

6.  Based on the p-value in Part I – Question 5, what is the conclusion of the test? Assume a = 5%. Did the change in manufacturer have any effect on the average number of home runs hit per game per team? (circle one)

Yes / No

Part II. After the football team once again lost a game to the college’s arch rival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A random sample of 100 alumni from the population of all living alumni was taken. 64 of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach.

7.  Construct a 95% confidence interval for p. Write your answer in the following format for full credit: ( point estimate ) ± ( margin of error )

Classroom version:
Textbook version:

8.  The association would like to reduce the margin of error to 0.05 for accuracy while maintaining a 95% confidence level. How large a sample is required? Use a conservative estimate for p = 0.5.

Classroom version:
Textbook version:

Hsieh, P-H 1