Topic 7 Review

The following table shows student’s math class and English class. We want to know if a student’s math class choice has an effect on their English class choice.

AP Stats / Stats / AP Calc / Total
AP English / 18 / 23
Regular English / 124 / 143
Total / 28 / 200

1. Complete the table so that all of the totals are correct.

2. Calculate the conditional distributions and complete the table below.

AP Stats / Stats / AP Calc
AP English
Regular English
Total

3. Create a segmented bar graph showing the conditional distributions of English class for each math class. Be sure to label appropriately.

4. Comment on any tendencies you see.

5. Suppose we wanted the math class choice and English class choice to be independent of each other. Complete the table so that these two variables are independent.

AP Stats / Stats / AP Calc / Total
AP English / 50
Regular English / 150
Total / 40 / 140 / 20 / 200

Out of 796 players in the NFL, 211 got injured last season. In comparison, there were 832 players in MLB and 105 were injured last season.

6. Find the conditional distributions of getting injured in each league.

7. Construct a segmented bar graph comparing the distributions of injuries in the 2 leagues.

8. Calculate the relative risk of playing football over baseball. What does that mean in context?

9. Construct a Simpson’s Paradox from the given chart. We want Hospital A to have a larger percentage of deaths overall, but Hospital B to have a larger percentage of deaths in each category.

Fair Condition / Poor Condition / Overall
Died in A
Total in A / 200 / 700 / 900
Proportion
Died in B
Total in B / 600 / 300 / 900
Proportion

Topic 7 Review

The following table shows student’s math class and English class. We want to know if a student’s math class choice has an effect on their English class choice.

AP Stats / Stats / AP Calc / Total
AP English / 18 / 23 / 16 / 57
Regular English / 10 / 124 / 9 / 143
Total / 28 / 147 / 25 / 200

1. Complete the table so that all of the totals are correct.

2. Calculate the conditional distributions and complete the table below.

AP Stats / Stats / AP Calc
AP English / .64 / .16 / .64
Regular English / .36 / .84 / .36
Total / 1 / 1 / 1

3. Create a segmented bar graph showing the conditional distributions of English class for each math class. Be sure to label appropriately.

4. Comment on any tendencies you see.

It appears that the students who take AP Math classes tend to take AP English more often than those who take regular stats.

5. Suppose we wanted the math class choice and English class choice to be independent of each other. Complete the table so that these two variables are independent.

AP Stats / Stats / AP Calc / Total
AP English / 10 / 35 / 5 / 50
Regular English / 30 / 105 / 15 / 150
Total / 40 / 140 / 20 / 200

Out of 796 players in the NFL, 211 got injured last season. In comparison, there were 832 players in MLB and 105 were injured last season.

6. Find the conditional distributions of getting injured in each league.

NFL / MLB / Total
Injured / 211 / 105 / 316
Not Injured / 585 / 727 / 1312
Total / 796 / 832 / 1628
NFL / MLB
Injured / .27 / .13
Not Injured / .73 / .87
Total / 1 / 1

7. Construct a segmented bar graph comparing the distributions of injuries in the 2 leagues.

8. Calculate the relative risk of playing football over baseball. What does that mean in context?

NFL players are about twice as likely to get injured than MLB players.

9. Construct a Simpson’s Paradox from the given chart. We want Hospital A to have a larger percentage of deaths overall, but Hospital B to have a larger percentage of deaths in each category.

Fair Condition / Poor Condition / Overall
Died in A / 45 / 255 / 300
Total in A / 200 / 700 / 900
Proportion / .23 / .36 / .33
Died in B / 180 / 120 / 280
Total in B / 600 / 300 / 900
Proportion / .30 / .40 / .31