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 0.8 of its customers are satisfied. In a random survey of 400 customers, 296 say they are satisfied. Find the test statistic z for H₀: p = 0.8.

p₀ = 0.8n = 400x = 296
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 12 mL. A sample of 100 bottles has a mean of 497.8 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 497.8 mLσ = 12 mLn = 100
z =
3.Medium
t −2.13102.131

A sample of 16 students has a mean score of 193 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 193s = 20n = 16
t =
4.Medium
−1.961.96z = ?

Two production lines make the same part. Line 1: a sample of 80 parts has mean length 147.5 mm, and the line's known standard deviation is 4 mm. Line 2: a sample of 100 parts has mean 150.6 mm, known standard deviation 12 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 80x̄₁ = 147.5 mmσ₁ = 4 mmn₂ = 100x̄₂ = 150.6 mmσ₂ = 12 mm
z =
5.Hard
H₀H₁μ₀x̄cμ₀ + 4α = 0.05βσ = 20, power 90%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 4 units with a power of 90%. The standard deviation is 20. Find the minimum sample size n.

α = 0.05power = 90%δ = 4σ = 20zα = 1.645zβ = 1.282
n =
6.Hard
z −2.57602.576

A sample of 25 measurements has mean 198.3. The population standard deviation is 12. Find the upper limit U of the 99% confidence interval for the mean.

x̄ = 198.3σ = 12n = 2599%
U =

Answer key

  1. 1. z = −3
  2. 2. z = −1.833
  3. 3. t = −1.4
  4. 4. z = −2.421
  5. 5. n = 215
  6. 6. U = 204.5

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