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 100 mL on average. The standard deviation is known to be 20 mL. A sample of 64 bottles has a mean of 92.25 mL. Find the test statistic z for H₀: μ = 100.

μ₀ = 100 mLx̄ = 92.25 mLσ = 20 mLn = 64
z =
2.Easy
−1.9601.96z = ?

A company claims that a proportion of 0.7 of its customers are satisfied. In a random survey of 120 customers, 69 say they are satisfied. Find the test statistic z for H₀: p = 0.7.

p₀ = 0.7n = 120x = 69
z =
3.Medium
t −2.01102.011

A sample of 49 students has a mean score of 49.2 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 49.2s = 4n = 49
t =
4.Medium
t −2.06402.064

A sample of 25 students has a mean score of 501.7 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 501.7s = 5n = 25
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 1.5α = 0.01βσ = 11, power 80%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 1.5 units with a power of 80%. The standard deviation is 11. Find the minimum sample size n.

α = 0.01power = 80%δ = 1.5σ = 11zα = 2.326zβ = 0.842
n =
6.Hard
−1.961.96z = ?

In a trial, 135 of 300 patients on treatment A recover, and 40 of 120 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 135n₁ = 300x₂ = 40n₂ = 120
z =

Answer key

  1. 1. z = −3.1
  2. 2. z = −2.988
  3. 3. t = −1.4
  4. 4. t = 1.7
  5. 5. n = 540
  6. 6. z = 2.191

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