In comparing flea rates between dogs and cats, the null hypothesis states that the proportions are equal. Which expression represents this null hypothesis in terms of p_dogs and p_cats?

In comparing flea rates between dogs and cats, the null hypothesis states that the proportions are equal. Which expression represents this null hypothesis in terms of p_dogs and p_cats?

• A. p_dogs = p_cats
• B. p_dogs ≠ p_cats
• C. p_dogs < p_cats
• D. p_dogs > p_cats

Answer: (A)

When comparing two proportions, the null hypothesis holds that there is no difference between the groups, so the two population proportions are equal. The expression that represents this is p_dogs = p_cats. Interpreted this way, any observed difference in flea rates would be due to random sampling variation under the assumption of equality. If you were testing for a difference in a specific direction, you’d use a one-sided alternative like p_dogs > p_cats or p_dogs < p_cats, but those describe alternatives to the null rather than the null itself. If you’re testing for any difference in either direction, the corresponding alternative would be p_dogs ≠ p_cats.

When comparing two proportions, the null hypothesis holds that there is no difference between the groups, so the two population proportions are equal. The expression that represents this is p_dogs = p_cats. Interpreted this way, any observed difference in flea rates would be due to random sampling variation under the assumption of equality. If you were testing for a difference in a specific direction, you’d use a one-sided alternative like p_dogs > p_cats or p_dogs < p_cats, but those describe alternatives to the null rather than the null itself. If you’re testing for any difference in either direction, the corresponding alternative would be p_dogs ≠ p_cats.