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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Name: ____________________   Date: ____________

1.Easy
−1.541.54p = ?

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = 1.54. Find the p-value p.

z = 1.54H₁: μ ≠ μ₀
p =
2.Easy
−1.291.29p = ?

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = 1.29. Find the p-value p.

z = 1.29H₁: μ ≠ μ₀
p =
3.Medium
−1.961.96z = ?

Two production lines make the same part. Line 1: a sample of 60 parts has mean length 67.5 mm, and the line's known standard deviation is 6 mm. Line 2: a sample of 100 parts has mean 65.7 mm, known standard deviation 13 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 60x̄₁ = 67.5 mmσ₁ = 6 mmn₂ = 100x̄₂ = 65.7 mmσ₂ = 13 mm
z =
4.Medium
t −1.98401.984

A sample of 100 students has a mean score of 79.8 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 79.8s = 20n = 100
t =
5.Hard
σ = 15, n = ?x̄ − Ex̄ + Ex̄E = 1.590%

How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 1.5? The standard deviation is 15. Find the smallest sample size n.

σ = 15E = 1.590%
n =
6.Hard
z −2.57602.576

A sample of 25 measurements has mean 97.9. The population standard deviation is 5. Find the upper limit U of the 99% confidence interval for the mean.

x̄ = 97.9σ = 5n = 2599%
U =

Answer key

  1. 1. p = 0.1236
  2. 2. p = 0.1971
  3. 3. z = 1.189
  4. 4. t = 2.4
  5. 5. n = 271
  6. 6. U = 100.5

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