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, 133 say they are satisfied. Find the test statistic z for H₀: p = 0.4.

p₀ = 0.4n = 400x = 133
z =
2.Easy
1.74p = ?

A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.74. Find the p-value p.

z = 1.74H₁: μ > μ₀
p =
3.Medium
−1.961.96z = ?

Two production lines make the same part. Line 1: a sample of 30 parts has mean length 136 mm, and the line's known standard deviation is 6 mm. Line 2: a sample of 30 parts has mean 133.2 mm, known standard deviation 6 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 30x̄₁ = 136 mmσ₁ = 6 mmn₂ = 30x̄₂ = 133.2 mmσ₂ = 6 mm
z =
4.Medium
t −2.0302.03

A sample of 36 students has a mean score of 72.6 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 72.6s = 8n = 36
t =
5.Hard
z −1.64501.645

A sample of 25 measurements has mean 73.5. The population standard deviation is 15. Find the lower limit L of the 90% confidence interval for the mean.

x̄ = 73.5σ = 15n = 2590%
L =
6.Hard
H₀H₁μ₀x̄cμ₀ + 2α = 0.05βσ = 15, power 80%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 2 units with a power of 80%. The standard deviation is 15. Find the minimum sample size n.

α = 0.05power = 80%δ = 2σ = 15zα = 1.645zβ = 0.842
n =

Answer key

  1. 1. z = −2.756
  2. 2. p = 0.04093
  3. 3. z = 1.807
  4. 4. t = −1.8
  5. 5. L = 68.56
  6. 6. n = 348

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