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 z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.87. Find the p-value p.

z = 1.87H₁: μ > μ₀

p =

2.Easy

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = −2.3. Find the p-value p.

z = −2.3H₁: μ ≠ μ₀

p =

3.Medium

A sample of 25 students has a mean score of 497.9 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 497.9s = 4n = 25

t =

4.Medium

Two teaching methods are compared. Group 1: 7 students, mean score 88, standard deviation 10. Group 2: 14 students, mean score 76.3, standard deviation 5.5. 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 = 7x̄₁ = 88s₁ = 10n₂ = 14x̄₂ = 76.3s₂ = 5.5

t =

5.Hard

A one-sided z test of H₀: μ = 50 against H₁: μ < 50 is done at α = 0.05 with a sample of 100; the standard deviation is known to be 5. In reality the mean is 49.35. Find the probability of a Type II error β in percent.

μ₀ = 50μ = 49.35σ = 5n = 100α = 0.05

β = %

6.Hard

How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 2? The standard deviation is 8. Find the smallest sample size n.

σ = 8E = 290%

n =

Answer key

1. p = 0.03074
2. p = 0.02145
3. t = −2.625
4. t = 3.496
5. β = 63.5 %
6. n = 44

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