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.

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1.Easy

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 71.33 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 71.33 mLσ = 10 mLn = 36

z =

2.Easy

A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 12 mL. A sample of 36 bottles has a mean of 495.6 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 495.6 mLσ = 12 mLn = 36

z =

3.Medium

A sample of 36 students has a mean score of 204 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 204s = 10n = 36

t =

4.Medium

A sample of 81 students has a mean score of 97.07 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 97.07s = 12n = 81

t =

5.Hard

A one-sided z test of H₀: μ = 80 against H₁: μ > 80 is done at α = 0.05 with a sample of 64; the standard deviation is known to be 8. In reality the mean is 82.6. Find the power 1 − β of the test in percent.

μ₀ = 80μ = 82.6σ = 8n = 64α = 0.05

1 − β = %

6.Hard

A sample of 16 measurements has mean 70.3. The population standard deviation is 10. Find the upper limit U of the 99% confidence interval for the mean.

x̄ = 70.3σ = 10n = 1699%

U =

Answer key

1. z = −2.202
2. z = −2.2
3. t = 2.4
4. t = −2.198
5. 1 − β = 83.02 %
6. U = 76.74

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