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
z −1.9601.96

A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 10 mL. A sample of 36 bottles has a mean of 72.67 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 72.67 mLσ = 10 mLn = 36
z =
2.Easy
1.48p = ?

A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.48. Find the p-value p.

z = 1.48H₁: μ > μ₀
p =
3.Medium
−2.462.46p = ?

The mean of a population is claimed to be 50; the population standard deviation is known to be 6. A random sample of 144 observations has a mean of 48.77. Test H₀: μ = 50 against H₁: μ ≠ 50. Find the p-value p.

μ₀ = 50σ = 6n = 144x̄ = 48.77H₁: μ ≠ μ₀
p =
4.Medium
t −2.13102.131

A sample of 16 students has a mean score of 497.8 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 497.8s = 4n = 16
t =
5.Hard
σ = 15, n = ?x̄ − Ex̄ + Ex̄E = 2.599%

How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 2.5? The standard deviation is 15. Find the smallest sample size n.

σ = 15E = 2.599%
n =
6.Hard
−1.961.96z = ?

In a trial, 138 of 250 patients on treatment A recover, and 50 of 100 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 138n₁ = 250x₂ = 50n₂ = 100
z =

Answer key

  1. 1. z = −1.398
  2. 2. p = 0.06944
  3. 3. p = 0.01389
  4. 4. t = −2.2
  5. 5. n = 239
  6. 6. z = 0.8814

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