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AP Statistics Confidence Intervals for a Mean — practice questions

Explore 2 free Confidence Intervals for a Mean questions in AP Statistics Statistics. Open each question or exercise to read its content, reference answers and available explanation.

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Confidence Intervals for a Mean questions and exercises with answers

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A sample produces x-bar = 7 with an error bound of EBM = 2.5. What is the resulting confidence interval?Read the answer and worked solution →Continuing the exam-score example, σ = 3, n = 36, x-bar = 68, and z(0.05) = 1.645 for a 90% confidence level. What is the resulting confidence interval?Read the answer and worked solution →

Worked practice questions

A sample produces x-bar = 7 with an error bound of EBM = 2.5. What is the resulting confidence interval?

  1. (2.5, 7.0)
  2. (7.0, 9.5)
  3. (4.5, 9.5)
  4. (4.5, 7.0)
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Correct answer: C. (4.5, 9.5)

1. A confidence interval takes the form (x-bar - EBM, x-bar + EBM). 2. Lower bound: 7 - 2.5 = 4.5. 3. Upper bound: 7 + 2.5 = 9.5. 4. Options B and D only apply the error bound to one side of x-bar instead of both, so they are incomplete. _Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.1 A Single Population Mean using the Normal Distribution_

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Continuing the exam-score example, σ = 3, n = 36, x-bar = 68, and z(0.05) = 1.645 for a 90% confidence level. What is the resulting confidence interval?

  1. (67.18, 68.82)
  2. (65.00, 71.00)
  3. (68.00, 71.65)
  4. (64.36, 71.65)
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Correct answer: A. (67.18, 68.82)

1. Compute EBM = z(σ/sqrt(n)) = (1.645)(3/sqrt(36)) = (1.645)(0.5) = 0.8225. 2. Lower bound: 68 - 0.8225 = 67.1775, which rounds to 67.18. 3. Upper bound: 68 + 0.8225 = 68.8225, which rounds to 68.82. 4. Option D doubles the error bound by mistake, giving a needlessly wide interval. _Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.1 A Single Population Mean using the Normal Distribution_

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