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 75 mL on average. The standard deviation is known to be 4 mL. A sample of 16 bottles has a mean of 76.2 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 76.2 mLσ = 4 mLn = 16
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 8 mL. A sample of 64 bottles has a mean of 77.4 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 77.4 mLσ = 8 mLn = 64
z =
3.Medium
t −1.99801.998

A sample of 64 students has a mean score of 100.9 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 100.9s = 10n = 64
t =
4.Medium
t −2.06402.064

A sample of 25 students has a mean score of 81.8 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 81.8s = 20n = 25
t =
5.Hard
σ = 5, n = ?x̄ − Ex̄ + Ex̄E = 0.590%

How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 0.5? The standard deviation is 5. Find the smallest sample size n.

σ = 5E = 0.590%
n =
6.Hard
−1.961.96z = ?

In a trial, 130 of 200 patients on treatment A recover, and 40 of 80 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 130n₁ = 200x₂ = 40n₂ = 80
z =

Answer key

  1. 1. z = 1.2
  2. 2. z = 2.4
  3. 3. t = 0.72
  4. 4. t = 1.7
  5. 5. n = 271
  6. 6. z = 2.322

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