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
−1.9601.96z = ?

A company claims that a proportion of 0.4 of its customers are satisfied. In a random survey of 400 customers, 137 say they are satisfied. Find the test statistic z for H₀: p = 0.4.

p₀ = 0.4n = 400x = 137
z =
2.Easy
−2.332.33p = ?

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = 2.33. Find the p-value p.

z = 2.33H₁: μ ≠ μ₀
p =
3.Medium
t −2.13102.131

A sample of 16 students has a mean score of 209 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 209s = 15n = 16
t =
4.Medium
t −1.9901.99

A sample of 81 students has a mean score of 72.11 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 72.11s = 10n = 81
t =
5.Hard
−1.961.96z = ?

In a trial, 50 of 250 patients on treatment A recover, and 44 of 150 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 50n₁ = 250x₂ = 44n₂ = 150
z =
6.Hard
μ₀x̄c

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 9. In reality the mean is 497. Find the power 1 − β of the test in percent.

μ₀ = 500μ = 497σ = 9n = 36α = 0.01
1 − β = %

Answer key

  1. 1. z = −2.347
  2. 2. p = 0.01981
  3. 3. t = 2.4
  4. 4. t = −2.601
  5. 5. z = −2.131
  6. 6. 1 − β = 37.22 %

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