In this exercise, you will solve three questions, where you will be asked to calculate a linear correlation coefficient and determine whether there is a linear correlation between the two given variables.
Solve the following problems:
- Listed below are baseball team statistics, consisting of the proportions of wins and the result of this difference: Difference (number of runs scored) - (number of runs allowed).
The statistics are from a recent year, and the teams are NY-Yankees, Toronto, Boston, Cleveland, Texas, Houston, San Francisco, and Kansas City.
|
Difference
|
163
|
55
|
-5
|
88
|
51
|
16
|
-214
|
|
Wins
|
0.599
|
0.537
|
0.531
|
0.481
|
0.494
|
0.506
|
0.383
|
o Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from Table VI, Appendix A, p. A-14, of your textbook Elementary Statistics. Use α = 0.05.
o Is there sufficient evidence to conclude that there is a linear correlation between the proportion of wins and the above difference?
- A classic application of correlation involves the association between temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 minute and the corresponding temperatures in °F:
|
Chirps in 1 Min
|
882
|
1188
|
1104
|
864
|
1200
|
1032
|
960
|
900
|
|
Temperature(°F)
|
69.7
|
93.3
|
84.3
|
76.3
|
88.6
|
82.6
|
71.6
|
79.6
|
o Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from Table VI, Appendix A, p. A-14, of your textbook Elementary Statistics. Use α = 0.05.
o Is there a linear correlation between the number of chirps in 1 minute and the temperature?
- Given below is a control chart for the temperature of a freezer unit in a restaurant. The owner of the restaurant is deciding whether or not to buy a new unit. The two charts display the temperature for the past two weeks. Write a paragraph analyzing the control charts and argue whether the owner should buy a new unit or not.
Submission Requirements:
- Submit your work in a single Microsoft Word or Excel document.
- The answer to each question should be supported with an appropriate rationale or the correct steps.