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 worksheet Practise 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

A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −1.03. Find the p-value p.

z = −1.03H₁: μ < μ₀

p =

2.Easy

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 8 mL. A sample of 49 bottles has a mean of 47.49 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 47.49 mLσ = 8 mLn = 49

z =

3.Medium

7 employees take a typing test before and after a training course. For each person the difference d = after − before (words per minute) is recorded. The mean difference is −12.59 and the standard deviation of the differences is 11.9. Find the paired test statistic t for H₀: μ_d = 0.

n = 7d̄ = −12.59s_d = 11.9

t =

4.Medium

The mean of a population is claimed to be 120; the population standard deviation is known to be 25. A random sample of 100 observations has a mean of 124.4. Test H₀: μ = 120 against H₁: μ ≠ 120. Find the p-value p.

μ₀ = 120σ = 25n = 100x̄ = 124.4H₁: μ ≠ μ₀

p =

5.Hard

How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 2? The standard deviation is 15. Find the smallest sample size n.

σ = 15E = 295%

n =

6.Hard

How large must a sample be so that the 95% 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 = 2.595%

n =

Answer key

1. p = 0.1515
2. z = −2.196
3. t = −2.799
4. p = 0.07841
5. n = 217
6. n = 139

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