Hypothesis tests & confidence intervals worksheet with answers

Free printable Hypothesis tests & confidence intervals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
z −1.9601.96

A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 20 mL. A sample of 36 bottles has a mean of 209.7 mL. Find the test statistic z for H₀: μ = 200.

μ₀ = 200 mLx̄ = 209.7 mLσ = 20 mLn = 36
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 12 mL. A sample of 16 bottles has a mean of 56.3 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 56.3 mLσ = 12 mLn = 16
z =
3.Medium
−2.2012.201t = ?df = 11

12 employees take a typing test before and after a training course. For each person the difference d = after − before (words per minute) is recorded. The mean difference is −1.29 and the standard deviation of the differences is 2.8. Find the paired test statistic t for H₀: μd = 0.

n = 12d̄ = −1.29sd = 2.8
t =
4.Medium
t −2.13102.131

A sample of 16 students has a mean score of 496.9 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 496.9s = 4n = 16
t =
5.Hard
σ = 4, n = ?x̄ − Ex̄ + Ex̄E = 1.590%

How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 1.5? The standard deviation is 4. Find the smallest sample size n.

σ = 4E = 1.590%
n =
6.Hard
μ₀x̄c

A one-sided z test of H₀: μ = 500 against H₁: μ > 500 is done at α = 0.05 with a sample of 100; the standard deviation is known to be 10. In reality the mean is 502.8. Find the probability of a Type II error β in percent.

μ₀ = 500μ = 502.8σ = 10n = 100α = 0.05
β = %

Answer key

  1. 1. z = 2.91
  2. 2. z = 2.1
  3. 3. t = −1.596
  4. 4. t = −3.1
  5. 5. n = 20
  6. 6. β = 12.4 %

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