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
−1.731.73p = ?

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = −1.73. Find the p-value p.

z = −1.73H₁: μ ≠ μ₀
p =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 10 mL. A sample of 16 bottles has a mean of 205.3 mL. Find the test statistic z for H₀: μ = 200.

μ₀ = 200 mLx̄ = 205.3 mLσ = 10 mLn = 16
z =
3.Medium
t −2.06402.064

A sample of 25 students has a mean score of 73.6 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 73.6s = 5n = 25
t =
4.Medium
−1.961.96z = ?

Two production lines make the same part. Line 1: a sample of 80 parts has mean length 47 mm, and the line's known standard deviation is 19 mm. Line 2: a sample of 80 parts has mean 42.9 mm, known standard deviation 3 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 80x̄₁ = 47 mmσ₁ = 19 mmn₂ = 80x̄₂ = 42.9 mmσ₂ = 3 mm
z =
5.Hard
H₀H₁μ₀x̄cμ₀ + 1.5α = 0.01βσ = 6, 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 6. Find the minimum sample size n.

α = 0.01power = 90%δ = 1.5σ = 6zα = 2.326zβ = 1.282
n =
6.Hard
μ₀x̄c

A one-sided z test of H₀: μ = 500 against H₁: μ > 500 is done at α = 0.01 with a sample of 25; the standard deviation is known to be 7.5. In reality the mean is 505.55. Find the probability of a Type II error β in percent.

μ₀ = 500μ = 505.55σ = 7.5n = 25α = 0.01
β = %

Answer key

  1. 1. p = 0.08363
  2. 2. z = 2.12
  3. 3. t = −1.4
  4. 4. z = 1.906
  5. 5. n = 209
  6. 6. β = 8.472 %

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