What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 12 randomly selected games are shown below.   Attendance 50 13 54 34 31 60 60 31 41 42 48 59 Runs 7 5 4 7 3 8 10 3 4

What is the relationship between the attendance at a major league ball game and the total number of runs scored? Attendance figures (in thousands) and the runs scored for 12 randomly selected games are shown below.

1. Find the correlation coefficient:  r=r=    Round to 2 decimal places.
2. The null and alternative hypotheses for correlation are:
   H0:H0:      == 0
   H1:H1:       ≠≠ 0    
   The p-value is:    (Round to four decimal places)
   
   
3. Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.
   
   • There is statistically significant evidence to conclude that a game with a higher attendance will have more runs scored than a game with lower attendance.
   • There is statistically significant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the regression line is useful.
   • There is statistically insignificant evidence to conclude that there is a correlation between the attendance of baseball games and the runs scored. Thus, the use of the regression line is not appropriate.
   • There is statistically significant evidence to conclude that a game with higher attendance will have fewer runs scored than a game with lower attendance.
4.  r2r2 =  (Round to two decimal places)  (Round to two decimal places)
5.  Interpret r2r2 :  
   • There is a large variation in the runs scored in baseball games, but if you only look at games with a fixed attendance, this variation on average is reduced by 36%.
   • There is a 36% chance that the regression line will be a good predictor for the runs scored based on the attendance of the game.
   • Given any fixed attendance, 36% of all of those games will have the predicted number of runs scored.
   • 36% of all games will have the average number of runs scored.
6. The equation of the linear regression line is:   
   ˆyy^ =  + xx   (Please show your answers to two decimal places)  
   
   
7. Use the model to predict the runs scored at a game that has an attendance of 21,000 people.
   Runs scored =  (Please round your answer to the nearest whole number.)  
   
   
8. Interpret the slope of the regression line in the context of the question:  
   • The slope has no practical meaning since the total number runs scored in a game must be positive.
   • For every additional thousand people who attend a game, there tends to be an average increase of 0.09 runs scored.
   • As x goes up, y goes up.
   
   
   
9. Interpret the y-intercept in the context of the question:
   • If the attendance of a baseball game is 0, then 2 runs will be scored.
   • The average runs scored is predicted to be 2.
   • The y-intercept has no practical meaning for this study.
   • The best prediction for a game with 0 attendance is that there will be 2 runs scored.