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
−1.141.14p = ?

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = −1.14. Find the p-value p.

z = −1.14H₁: μ ≠ μ₀
p =
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 4 mL. A sample of 49 bottles has a mean of 50.97 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 50.97 mLσ = 4 mLn = 49
z =
3.Medium
t −2.01102.011

A sample of 49 students has a mean score of 98.74 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 98.74s = 4n = 49
t =
4.Medium
t −2.01102.011

A sample of 49 students has a mean score of 120.7 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 120.7s = 4n = 49
t =
5.Hard
σ = 12, n = ?x̄ − Ex̄ + Ex̄E = 195%

How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 1? The standard deviation is 12. Find the smallest sample size n.

σ = 12E = 195%
n =
6.Hard
σ = 8, 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 8. Find the smallest sample size n.

σ = 8E = 1.590%
n =

Answer key

  1. 1. p = 0.2543
  2. 2. z = 1.697
  3. 3. t = −2.205
  4. 4. t = 1.225
  5. 5. n = 554
  6. 6. n = 77

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