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
−2.222.22p = ?

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = 2.22. Find the p-value p.

z = 2.22H₁: μ ≠ μ₀
p =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 4 mL. A sample of 64 bottles has a mean of 98.9 mL. Find the test statistic z for H₀: μ = 100.

μ₀ = 100 mLx̄ = 98.9 mLσ = 4 mLn = 64
z =
3.Medium
t −2.06402.064

A sample of 25 students has a mean score of 73.2 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 73.2s = 5n = 25
t =
4.Medium
t −2.0302.03

A sample of 36 students has a mean score of 50.47 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 50.47s = 4n = 36
t =
5.Hard
−1.961.96z = ?

In a trial, 50 of 250 patients on treatment A recover, and 14 of 100 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 50n₁ = 250x₂ = 14n₂ = 100
z =
6.Hard
σ = 5, n = ?x̄ − Ex̄ + Ex̄E = 0.590%

How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 0.5? The standard deviation is 5. Find the smallest sample size n.

σ = 5E = 0.590%
n =

Answer key

  1. 1. p = 0.02642
  2. 2. z = −2.2
  3. 3. t = −1.8
  4. 4. t = 0.705
  5. 5. z = 1.312
  6. 6. n = 271

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