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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
−1.9601.96z = ?

A company claims that a proportion of 0.3 of its customers are satisfied. In a random survey of 200 customers, 70 say they are satisfied. Find the test statistic z for H₀: p = 0.3.

p₀ = 0.3n = 200x = 70
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 8 mL. A sample of 81 bottles has a mean of 48.76 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 48.76 mLσ = 8 mLn = 81
z =
3.Medium
t −1.9901.99

A sample of 81 students has a mean score of 46 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 46s = 20n = 81
t =
4.Medium
t −1.99801.998

A sample of 64 students has a mean score of 202.9 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 202.9s = 8n = 64
t =
5.Hard
μ₀x̄c

A one-sided z test of H₀: μ = 80 against H₁: μ > 80 is done at α = 0.05 with a sample of 64; the standard deviation is known to be 20. In reality the mean is 85.75. Find the probability of a Type II error β in percent.

μ₀ = 80μ = 85.75σ = 20n = 64α = 0.05
β = %
6.Hard
−1.961.96z = ?

In a trial, 38 of 150 patients on treatment A recover, and 60 of 150 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 38n₁ = 150x₂ = 60n₂ = 150
z =

Answer key

  1. 1. z = 1.543
  2. 2. z = −1.395
  3. 3. t = −1.8
  4. 4. t = 2.9
  5. 5. β = 25.62 %
  6. 6. z = −2.708

Full step-by-step solutions: practise this topic on examproblems.com.