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 120 mL on average. The standard deviation is known to be 4 mL. A sample of 81 bottles has a mean of 119 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 119 mLσ = 4 mLn = 81
z =
2.Easy
−1.9601.96z = ?

A company claims that a proportion of 0.25 of its customers are satisfied. In a random survey of 120 customers, 37 say they are satisfied. Find the test statistic z for H₀: p = 0.25.

p₀ = 0.25n = 120x = 37
z =
3.Medium
t −1.98401.984

A sample of 100 students has a mean score of 122 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 122s = 12n = 100
t =
4.Medium
t −2.13102.131

A sample of 16 students has a mean score of 197.2 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 197.2s = 8n = 16
t =
5.Hard
z −1.9601.96

A sample of 100 measurements has mean 495.5. The population standard deviation is 15. Find the upper limit U of the 95% confidence interval for the mean.

x̄ = 495.5σ = 15n = 10095%
U =
6.Hard
μ₀x̄c

A one-sided z test of H₀: μ = 80 against H₁: μ > 80 is done at α = 0.01 with a sample of 64; the standard deviation is known to be 12. In reality the mean is 83. Find the probability of a Type II error β in percent.

μ₀ = 80μ = 83σ = 12n = 64α = 0.01
β = %

Answer key

  1. 1. z = −2.25
  2. 2. z = 1.476
  3. 3. t = 1.667
  4. 4. t = −1.4
  5. 5. U = 498.4
  6. 6. β = 62.78 %

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