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  1. Subjects ›
  2. AP Statistics ›
  3. Question of the Day

AP Statistics Question of the Day

AP Statistics Question of the Day

Answer today's AP Statistics question, reveal the full explanation, then keep the streak going with a new question every day.

A streaming service believes that the proportion of users who watch content on a mobile device is different from 35%. The company randomly samples 160 users and finds that 44 primarily watch on mobile (p^=0.275\hat{p}=0.275p^​=0.275). Which hypotheses are appropriate for testing the company’s belief?

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Question of the Day

A streaming service believes that the proportion of users who watch content on a mobile device is different from 35%. The company randomly samples 160 users and finds that 44 primarily watch on mobile (p^=0.275\hat{p}=0.275p^​=0.275). Which hypotheses are appropriate for testing the company’s belief?

  1. H0:p=0.35Ha:p≠0.35H_0: p=0.35\quad H_a: p\ne0.35H0​:p=0.35Ha​:p=0.35 (correct answer)
  2. H0:p=0.275Ha:p≠0.275H_0: p=0.275\quad H_a: p\ne0.275H0​:p=0.275Ha​:p=0.275
  3. H0:p^=0.35Ha:p^≠0.35H_0: \hat{p}=0.35\quad H_a: \hat{p}\ne0.35H0​:p^​=0.35Ha​:p^​=0.35
  4. H0:p=0.35Ha:p<0.35H_0: p=0.35\quad H_a: p<0.35H0​:p=0.35Ha​:p<0.35
  5. H0:p≠0.35Ha:p=0.35H_0: p\ne0.35\quad H_a: p=0.35H0​:p=0.35Ha​:p=0.35

Explanation: The skill here is crafting hypotheses for a one-proportion z-test in AP Statistics to examine if p differs from 0.35. The correct setup is H0: p = 0.35 and Ha: p ≠ 0.35, capturing the two-sided nature of 'different from,' as in choice A. A distractor is choice C, which uses ˆp incorrectly. Choice D uses a one-sided alternative, but 'different' requires checking both directions. For a mini-lesson, two-sided alternatives use ≠ for claims of difference or inaccuracy. Null is always equality, focused on p. Sample data tests the hypotheses but doesn't appear in them.