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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Name: ____________________   Date: ____________

1.Easy
1.09p = ?

A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.09. Find the p-value p.

z = 1.09H₁: μ > μ₀
p =
2.Easy
−1.82p = ?

A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −1.82. Find the p-value p.

z = −1.82H₁: μ < μ₀
p =
3.Medium
−2.0932.093t = ?df = 19

20 employees take a typing test before and after a training course. For each person the difference d = after − before (words per minute) is recorded. The mean difference is −3.49 and the standard deviation of the differences is 5.2. Find the paired test statistic t for H₀: μd = 0.

n = 20d̄ = −3.49sd = 5.2
t =
4.Medium
t −2.06402.064

A sample of 25 students has a mean score of 47.4 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 47.4s = 5n = 25
t =
5.Hard
μ₀x̄c

A one-sided z test of H₀: μ = 200 against H₁: μ > 200 is done at α = 0.01 with a sample of 36; the standard deviation is known to be 6. In reality the mean is 203.5. Find the power 1 − β of the test in percent.

μ₀ = 200μ = 203.5σ = 6n = 36α = 0.01
1 − β = %
6.Hard
μ₀x̄c

A one-sided z test of H₀: μ = 500 against H₁: μ > 500 is done at α = 0.05 with a sample of 36; the standard deviation is known to be 12. In reality the mean is 502.2. Find the power 1 − β of the test in percent.

μ₀ = 500μ = 502.2σ = 12n = 36α = 0.05
1 − β = %

Answer key

  1. 1. p = 0.1379
  2. 2. p = 0.03438
  3. 3. t = −3.001
  4. 4. t = −2.6
  5. 5. 1 − β = 87.98 %
  6. 6. 1 − β = 29.29 %

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