The scholarship committee has two readers for each scholarship to promote equal grading. Sometimes, though the graders have different grading standards. We wish to investigate. Suppose, you have the following marks on 25 applications
| grader 1 | 3 | 5 | 5 | 4 | 5 | 5 | 3 | 5 | 3 | 4 | 3 | 5 | 4 | 3 | 5 | 4 | 5 | 5 | 5 | 3 | 3 | 5 | 3 | 4 | 5 |
| grader 2 | 4 | 4 | 2 | 1 | 4 | 2 | 3 | 5 | 3 | 2 | 4 | 2 | 5 | 2 | 3 | 5 | 3 | 3 | 4 | 3 | 4 | 4 | 4 | 2 | 3 |
Do the two graders grade similarly? What test will you use, why is it valid?
At the M&M’s factory, the ratio of Blue to Red to Green is 3:4:2. Suppose your bag of 30 M&Ms contains the following:
| Color | Blue | Red | Green |
| count | 10 | 10 | 10 |
Do a $\chi^2$ analysis to test if your bag comes from the distribution at the factory, or was perhaps tampered with. Are the assumptions met? (What are they?)
The key is Stat->table -> chis squared test.
Problem 10.16: You know
| Cause | 1990 percent | 1993 totals |
| Heart Disease | 33.5 | 739,860 |
| Cancer | 23.4 | 530,870 |
| Stroke | 6.7 | 149,740 |
| Accident | 4.3 | 88,630 |
| Lung Disease | 4.1 | 101,090 |
| Other | 28 | 657,810 |
Do the 1993 totals appear to come from the same distribution as 1990? Do a $\chi^2$ goodness of fit test.
Do seat belts work?
injury level
Seat Belt
| none | minimal | minor | major | |
| Yes | 12813 | 647 | 359 | 42 |
| No | 65,963 | 4000 | 2642 | 303 |
A superstitious student believes that the toss of the first coin, affects the toss of the second. She tosses her coin twice 30 times and found the following
Second Toss
First
| H | T | |
| H | 11 | 7 |
| T | 6 | 6 |
Does a $\chi^2$ test for independence lead the student to believe the coins are or are not independent. Explain.