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 200 mL on average. The standard deviation is known to be 10 mL. A sample of 100 bottles has a mean of 197.4 mL. Find the test statistic z for H₀: μ = 200.

μ₀ = 200 mLx̄ = 197.4 mLσ = 10 mLn = 100
z =
2.Easy
μ₀x̄c = ?α = 0.10

A machine is set to fill packs with a mean of 500 g; you suspect it underfills. The standard deviation is known to be 3 g. You will weigh a sample of 36 packs and test H₀: μ = 500 against H₁: μ < 500 at α = 0.10. Below which sample mean x̄c will you reject H₀?

μ₀ = 500 gσ = 3 gn = 36α = 0.10
x̄c = g
3.Medium
−2.0452.045t = ?df = 29

Two teaching methods are compared. Group 1: 13 students, mean score 82, standard deviation 3. Group 2: 18 students, mean score 84.2, standard deviation 4. Assume equal population variances and use the pooled two-sample t test. Find the test statistic t for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (group 1 minus group 2).

n₁ = 13x̄₁ = 82s₁ = 3n₂ = 18x̄₂ = 84.2s₂ = 4
t =
4.Medium
t −1.9901.99

A sample of 81 students has a mean score of 79.83 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 79.83s = 15n = 81
t =
5.Hard
σ = 15, n = ?x̄ − Ex̄ + Ex̄E = 0.599%

How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 0.5? The standard deviation is 15. Find the smallest sample size n.

σ = 15E = 0.599%
n =
6.Hard
σ = 10, n = ?x̄ − Ex̄ + Ex̄E = 299%

How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 2? The standard deviation is 10. Find the smallest sample size n.

σ = 10E = 299%
n =

Answer key

  1. 1. z = −2.6
  2. 2. x̄c = 499.4 g
  3. 3. t = −1.67
  4. 4. t = 2.898
  5. 5. n = 5973
  6. 6. n = 166

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