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 4 mL. A sample of 64 bottles has a mean of 76.2 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 76.2 mLσ = 4 mLn = 64

z =

2.Easy

A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 4 mL. A sample of 36 bottles has a mean of 117.9 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 117.9 mLσ = 4 mLn = 36

z =

3.Medium

A sample of 81 students has a mean score of 497.6 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 497.6s = 12n = 81

t =

4.Medium

A sample of 16 students has a mean score of 198.3 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 198.3s = 5n = 16

t =

5.Hard

A one-sided z test of H₀: μ = 200 against H₁: μ > 200 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 203.15. Find the probability of a Type II error β in percent.

μ₀ = 200μ = 203.15σ = 7.5n = 25α = 0.10

β = %

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 15. Find the smallest sample size n.

σ = 15E = 1.595%

n =

Answer key

1. z = 2.4
2. z = −3.15
3. t = −1.8
4. t = −1.36
5. β = 20.67 %
6. n = 385

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