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 100 mL on average. The standard deviation is known to be 10 mL. A sample of 25 bottles has a mean of 93.8 mL. Find the test statistic z for H₀: μ = 100.

μ₀ = 100 mLx̄ = 93.8 mLσ = 10 mLn = 25
z =
2.Easy
−2.14p = ?

A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −2.14. Find the p-value p.

z = −2.14H₁: μ < μ₀
p =
3.Medium
t −1.9901.99

A sample of 81 students has a mean score of 78.78 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 78.78s = 20n = 81
t =
4.Medium
t −1.98401.984

A sample of 100 students has a mean score of 502.6 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 502.6s = 15n = 100
t =
5.Hard
z −1.9601.96

A sample of 100 measurements has mean 98.8. The population standard deviation is 5. Find the upper limit U of the 95% confidence interval for the mean.

x̄ = 98.8σ = 5n = 10095%
U =
6.Hard
−1.961.96z = ?

In a trial, 35 of 100 patients on treatment A recover, and 92 of 200 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 35n₁ = 100x₂ = 92n₂ = 200
z =

Answer key

  1. 1. z = −3.1
  2. 2. p = 0.01618
  3. 3. t = 1.701
  4. 4. t = 1.733
  5. 5. U = 99.78
  6. 6. z = −1.818

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