What is the marginal proportion of students who own a pet?

Answer: 70/120 The marginal proportion uses the row/column total over the grand total: 70 owners out of 120 students.

What is the marginal proportion of Pop fans?

Answer: 50/100 = 0.50 Marginal proportion uses the row total over the grand total: 50/100 = 0.50.

Among those with allergies, what proportion was exposed?

Answer: 45/60 = 0.75 Conditioning on Allergy = Yes column total of 60: 45 of 60 had exposure, giving 0.75.

AP Statistics · Topic 2.2

Representing Two Categorical Variables Practice

Part of Exploring Two-Variable Data.(UNC-1.H)

Practice questions

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Sample questions

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Sample 1difficulty 1/5
$The two-way table shows pet ownership by grade.$
$What is the marginal proportion of students who own a pet?$
- A
  $40/60$
- B
  $40/120$
- C
  $70/120$
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- D
  $70/60$
Why
$The marginal proportion uses the row/column total over the grand total: 70 owners out of 120 students.$
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Sample 2difficulty 1/5
$The table shows music preference vs whether students play a sport.$
$What is the marginal proportion of Pop fans?$
- A
  $35/50 = 0.70$
- B
  $15/40 = 0.375$
- C
  $35/60 = 0.58$
- D
  $50/100 = 0.50$
  check_circle
Why
$Marginal proportion uses the row total over the grand total: 50/100 = 0.50.$
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Sample 3difficulty 2/5
$The table cross-classifies allergy by exposure.$
$Among those with allergies, what proportion was exposed?$
- A
  $60/500 = 0.12$
- B
  $200/500 = 0.40$
- C
  $45/60 = 0.75$
  check_circle
- D
  $45/200 = 0.225$
Why
$Conditioning on Allergy = Yes column total of 60: 45 of 60 had exposure, giving 0.75.$
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Sample 4difficulty 2/5
$A two-way table is used for$
- A
  $Two categorical variables$
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- B
  $Time series$
- C
  $One categorical variable$
- D
  $One quantitative variable$
Why
$Cells display joint counts of categories from two categorical variables.$
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Sample 5difficulty 2/5
$Bars show conditional percentage of "Yes" in three groups.$
$Which conclusion is supported?$
- A
  $Group is independent of response$
- B
  $Group sizes are equal$
- C
  $The Yes-rate depends on group; B has the highest, C the lowest$
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- D
  $All groups have equal Yes-rates$
Why
$The differing bar heights show different conditional proportions, indicating an association.$
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