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 company claims that a proportion of 0.3 of its customers are satisfied. In a random survey of 250 customers, 63 say they are satisfied. Find the test statistic z for H₀: p = 0.3.

p₀ = 0.3n = 250x = 63

z =

2.Easy

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = −1.97. Find the p-value p.

z = −1.97H₁: μ ≠ μ₀

p =

3.Medium

The mean of a population is claimed to be 50; the population standard deviation is known to be 30. A random sample of 144 observations has a mean of 44.25. Test H₀: μ = 50 against H₁: μ ≠ 50. Find the p-value p.

μ₀ = 50σ = 30n = 144x̄ = 44.25H₁: μ ≠ μ₀

p =

4.Medium

A sample of 36 students has a mean score of 49.25 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 49.25s = 5n = 36

t =

5.Hard

A one-sided z test of H₀: μ = 500 against H₁: μ < 500 is done at α = 0.01 with a sample of 36; the standard deviation is known to be 18. In reality the mean is 495.5. Find the power 1 − β of the test in percent.

μ₀ = 500μ = 495.5σ = 18n = 36α = 0.01

1 − β = %

6.Hard

A one-sided z test of H₀: μ = 200 against H₁: μ > 200 is done at α = 0.05 with a sample of 100; the standard deviation is known to be 30. In reality the mean is 209. Find the probability of a Type II error β in percent.

μ₀ = 200μ = 209σ = 30n = 100α = 0.05

β = %

Answer key

1. z = −1.656
2. p = 0.04884
3. p = 0.02145
4. t = −0.9
5. 1 − β = 20.44 %
6. β = 8.771 %

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