Chi Square Exercises
1. Exercise
A die is suspected of being biased. It is rolled 25 times with the following result:
| Outcome | Frequency |
|---|---|
| 1 | 9 |
| 2 | 4 |
| 3 | 1 |
| 4 | 8 |
| 5 | 3 |
| 6 | 0 |
Conduct a significance test to see if the die is biased. What Chi Square value do you get and how many degrees of freedom does it have? (relevant section)
2. Exercise
A recent experiment investigated the relationship between smoking and urinary incontinence. Of the 322 subjects in the study who were incontinent, 113 were smokers, 51 were former smokers, and 158 had never smoked. Of the 284 control subjects who were not incontinent, 68 were smokers, 23 were former smokers, and 193 had never smoked. (a) Create a table displaying this data. b) What is the expected frequency in each cell? (relevant section)
3. Exercise
At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem that random to you. You think it is a little fishy that sophomores organized the raffle and also won the most prizes. Your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors. Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values. (relevant section)
4. Exercise
Some parents of the West Bay little leaguers think that they are noticing a pattern. There seems to be a relationship between the number on the kids' jerseys and their position. These parents decide to record what they see. The hypothetical data appear below. Conduct a Chi Square test to determine if the parents' suspicion that there is a relationship between jersey number and position is right. Report your Chi Square and p values. (relevant section)
| Infield | Outfield | Pitcher | Total | |
|---|---|---|---|---|
| 0-9 | 12 | 5 | 5 | 22 |
| 10-19 | 5 | 10 | 2 | 17 |
| 20+ | 4 | 4 | 7 | 15 |
| Total | 21 | 19 | 14 | 54 |
Answers:
1) (a) Chi Square = 16.0, df = 5
2) (b) Incontinent/Smoker cell: 96.2
3) (b) p = .18
4) Chi Square = 10.2
