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 50 mL on average. The standard deviation is known to be 5 mL. A sample of 16 bottles has a mean of 52.63 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 52.63 mLσ = 5 mLn = 16
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 5 mL. A sample of 16 bottles has a mean of 496.1 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 496.1 mLσ = 5 mLn = 16
z =
3.Medium
t −2.06402.064

A sample of 25 students has a mean score of 113.4 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 113.4s = 15n = 25
t =
4.Medium
−1.961.96z = ?

Two production lines make the same part. Line 1: a sample of 30 parts has mean length 132 mm, and the line's known standard deviation is 17 mm. Line 2: a sample of 100 parts has mean 141.8 mm, known standard deviation 10 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 30x̄₁ = 132 mmσ₁ = 17 mmn₂ = 100x̄₂ = 141.8 mmσ₂ = 10 mm
z =
5.Hard
σ = 12, n = ?x̄ − Ex̄ + Ex̄E = 195%

How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 1? The standard deviation is 12. Find the smallest sample size n.

σ = 12E = 195%
n =
6.Hard
H₀H₁μ₀x̄cμ₀ + 1.5α = 0.01βσ = 7, power 90%, 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 90%. The standard deviation is 7. Find the minimum sample size n.

α = 0.01power = 90%δ = 1.5σ = 7zα = 2.326zβ = 1.282
n =

Answer key

  1. 1. z = 2.104
  2. 2. z = −3.12
  3. 3. t = −2.2
  4. 4. z = −3.005
  5. 5. n = 554
  6. 6. n = 284

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