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 50 mL on average. The standard deviation is known to be 15 mL. A sample of 81 bottles has a mean of 53.5 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 53.5 mLσ = 15 mLn = 81

z =

2.Easy

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 10 mL. A sample of 25 bottles has a mean of 46.4 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 46.4 mLσ = 10 mLn = 25

z =

3.Medium

A sample of 36 students has a mean score of 202.3 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 202.3s = 8n = 36

t =

4.Medium

A sample of 100 students has a mean score of 97.9 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 97.9s = 15n = 100

t =

5.Hard

A sample of 81 measurements has mean 70.2. The population standard deviation is 15. Find the upper limit U of the 95% confidence interval for the mean.

x̄ = 70.2σ = 15n = 8195%

U =

6.Hard

A one-sided z test of H₀: μ = 500 against H₁: μ < 500 is done at α = 0.10 with a sample of 25; the standard deviation is known to be 7.5. In reality the mean is 497.9. Find the probability of a Type II error β in percent.

μ₀ = 500μ = 497.9σ = 7.5n = 25α = 0.10

β = %

Answer key

1. z = 2.1
2. z = −1.8
3. t = 1.725
4. t = −1.4
5. U = 73.47
6. β = 45.3 %

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