Unit 3E

Unit 3E

How Numbers Can Deceive: Polygraphs, Mammograms, and More

Multiple Choice

11.) a. Which player had the higher batting average in the first half of the season?

• Josh

• Jude

Multiple Choice

11.) b. Which player had the higher batting average in the second half of the season?

• Josh

• Jude

Multiple Choice

11.) c. Which player had the higher overall batting average for the season?

• Josh

• Jude

Open Ended

11.) d. Briefly explain why the results might seem surprising or paradoxical.

Multiple Choice

13. a. Which state had the higher scores in both racial categories? Which state had the higher overall average across both racial categories?

• Nebraska

• New Jersey

Multiple Choice

13. a. Which state had the higher scores in both racial categories? Which state had the higher overall average across both racial categories?

• Nebraska

• New Jersey

Open Ended

13.) b. Explain how a state could score lower in both categories and still have a higher overall average.

Open Ended

13.) c. The following table gives the actual percentages of whites and nonwhites in each state. Use these percentages to verify that the overall average test score in Nebraska is 277, as claimed in the first table.

13.) c. The following table gives the actual percentages of whites and nonwhites in each state. Use these percentages to verify that the overall average test score in Nebraska is 277, as claimed in the first table.

• 87% of 281 and 13% of 250

• 0.87(281) + .13(250)

• 244.46 + 32.5 = 276.97

Open Ended

13.) d. Use the racial percentages to verify that the overall average test score in New Jersey is 272, as claimed in the first table.

13.) d. Use the racial percentages to verify that the overall average test score in New Jersey is 272, as claimed in the first table.

• 66% of 283 and 34% of 252

• 0.66(283) + 0.34(252)

• 186.78 + 85.68 = 272.46

Open Ended

13.) e. Briefly explain why the results might seem surprising or paradoxical.

Open Ended

17.) a. Verify that the numbers in the table are correct. Show your work.

17. a. Verify that the numbers in the table are correct. Show your work.

• incidence rate of breast cancer is 1%

• Out of entire population, how many had cancer $\frac{100}{10,000}=0.01=1\%$  

• mammogram is 90% accurate

• out of those that have cancer, how many did it pick up $\frac{90}{100}=0.90=90\%$  

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17.) b. Suppose a patient has a positive mammogram. What is the chance that she has cancer?

Looking only at the positive row:

 $\frac{90\ cancer\ present}{1080\ total\ tested\ positive}=0.083333$  

= 8.33%

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17.) d. Suppose a patient has a negative mammogram. What is the chance that she does have cancer?

Looking only at the negative mamm row:

 $\frac{8910\ no\ cancer}{8920\ total\ tested\ negative}=0.9988789$  

= 99.89%

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23. (First find the percentage wins)

a. Give numerical evidence to support the claim that Spelman College has a better team than Morehouse College.

b. Give numerical evidence to support the claim that Morehouse College has a better team than Spelman College.

c. Which claim do you think makes more sense? Why?

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Multiple Choice

a. Give numerical evidence to support the claim that Spelman College has a better team than Morehouse College.

• Look at wins separated into categories of home and away.

• Look at the total wins.

Multiple Choice

b. Give numerical evidence to support the claim that Morehouse College has a better team than Spelman College.

• Look at wins separated into categories of home and away.

• Look at the total wins.

Multiple Choice

c. Which claim do you think makes more sense? Why?

• Spelman (grouped home/away)

• Morehouse (totaled)