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 = −2.23. Find the p-value p.

z = −2.23H₁: μ < μ₀

p =

2.Easy

A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 8 mL. A sample of 36 bottles has a mean of 122.8 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 122.8 mLσ = 8 mLn = 36

z =

3.Medium

Two teaching methods are compared. Group 1: 11 students, mean score 71.5, standard deviation 7. Group 2: 6 students, mean score 67.6, standard deviation 7. Assume equal population variances and use the pooled two-sample t test. Find the test statistic t for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (group 1 minus group 2).

n₁ = 11x̄₁ = 71.5s₁ = 7n₂ = 6x̄₂ = 67.6s₂ = 7

t =

4.Medium

A sample of 64 students has a mean score of 70.88 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 70.88s = 15n = 64

t =

5.Hard

A sample of 49 measurements has mean 122.9. The population standard deviation is 10. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 122.9σ = 10n = 4999%

L =

6.Hard

How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 1.5? The standard deviation is 5. Find the smallest sample size n.

σ = 5E = 1.599%

n =

Answer key

1. p = 0.01287
2. z = 2.1
3. t = 1.098
4. t = −2.197
5. L = 119.2
6. n = 74

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