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 machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 8 mL. A sample of 81 bottles has a mean of 501.1 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 501.1 mLσ = 8 mLn = 81

z =

2.Easy

A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 5 mL. A sample of 16 bottles has a mean of 78.63 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 78.63 mLσ = 5 mLn = 16

z =

3.Medium

A sample of 16 students has a mean score of 45.5 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 45.5s = 20n = 16

t =

4.Medium

A sample of 81 students has a mean score of 98.28 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 98.28s = 5n = 81

t =

5.Hard

A one-sided z test at α = 0.05 must detect a shift of the mean of 3 units with a power of 80%. The standard deviation is 23. Find the minimum sample size n.

α = 0.05power = 80%δ = 3σ = 23z_α = 1.645z_β = 0.842

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 1.5? The standard deviation is 20. Find the smallest sample size n.

σ = 20E = 1.595%

n =

Answer key

1. z = 1.238
2. z = 2.904
3. t = −0.9
4. t = −3.096
5. n = 364
6. n = 683

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