In a study comparing the obedience of dogs and cats, it was found that 18 of 20 dogs came when called, whereas 1 of 20 cats did. Which of the following is most appropriate to test whether dogs are more obedient than cats?

Question

In a study comparing the obedience of dogs and cats, it was found that 18 of 20 dogs came when called, whereas 1 of 20 cats did.  Which of the following is most appropriate to test whether dogs are more obedient than cats?

BlackTom AI · Accepted Answer

Because the outcomes are binary (each animal either "came" or "did not come"), the relevant parameter for each group is a population proportion of obedience, not a mean. A test that compares two proportions is therefore appropriate.

1) Relevant knowledge points and concepts
- Binary (Bernoulli) data are summarized by proportions (p̂ = successes / n).  
- To compare two independent groups on binary outcomes, use a two-sample test for proportions (z-test approximation or an exact test like Fisher’s exact).  
- Tests comparing means (pooled or unpooled t-tests) assume continuous outcomes and are not appropriate for binary success/failure data.

2) Complete reasoning process step by step
- Compute sample proportions: p̂_dogs = 18/20 = 0.90; p̂_cats = 1/20 = 0.05.  
- The difference in sample proportions is 0.90 − 0.05 = 0.85, suggesting dogs are much more obedient.

3) Intermediate calculations (for the two-proportion z-test illustration)
- Pooled proportion p̂ = (18 + 1) / (20 + 20) = 19/40 = 0.475.  
- Standard error = sqrt[ p̂(1 − p̂) (1/n1 + 1/n2) ] = sqrt[0.475×0.525×(1/20+1/20)]  
  = sqrt[0.249375×0.1] = sqrt[0.0249375] ≈ 0.1579.  
- Z = (0.90 − 0.05) / 0.1579 ≈ 0.85 / 0.1579 ≈ 5.39 (very large → p-value ≈ 0).

4) Why the correct answer is correct
- The data type (success/failure) makes the parameter of interest a proportion; therefore a hypothesis test comparing two proportions directly addresses whether the dog obedience proportion exceeds the cat obedience proportion.

5) Why the other options are incorrect
- Hypothesis tests comparing two means (pooled or unpooled) require continuous numeric measurements and compare means, not proportions; they are inappropriate for binary outcome data. The pooled/unpooled distinction refers to variance assumptions for continuous data, not relevant here.

6) Conclusion
- The most appropriate test is a hypothesis test comparing two proportions, which matches the provided answer.

In a study comparing the obedience of dogs and cats, it was found that 18 of 20 dogs came when called, whereas 1 of 20 cats did. Which of the following is most appropriate to test whether dogs are more obedient than cats?单项选择题

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