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
z −1.9601.96

A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 20 mL. A sample of 36 bottles has a mean of 507 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 507 mLσ = 20 mLn = 36
z =
2.Easy
−0.830.83p = ?

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = 0.83. Find the p-value p.

z = 0.83H₁: μ ≠ μ₀
p =
3.Medium
t −2.0302.03

A sample of 36 students has a mean score of 101.1 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 101.1s = 4n = 36
t =
4.Medium
t −2.06402.064

A sample of 25 students has a mean score of 71.64 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 71.64s = 12n = 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 100; the standard deviation is known to be 10. In reality the mean is 196.3. Find the power 1 − β of the test in percent.

μ₀ = 200μ = 196.3σ = 10n = 100α = 0.01
1 − β = %
6.Hard
−1.961.96z = ?

In a trial, 53 of 150 patients on treatment A recover, and 25 of 80 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 53n₁ = 150x₂ = 25n₂ = 80
z =

Answer key

  1. 1. z = 2.1
  2. 2. p = 0.4065
  3. 3. t = 1.65
  4. 4. t = −1.4
  5. 5. 1 − β = 91.53 %
  6. 6. z = 0.623

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