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 15 mL. A sample of 100 bottles has a mean of 197.3 mL. Find the test statistic z for H₀: μ = 200.

μ₀ = 200 mLx̄ = 197.3 mLσ = 15 mLn = 100
z =
2.Easy
μ₀x̄c = ?α = 0.05

A supplier claims that the mean breaking strength of a cable is 500 kN; you suspect it is higher. The standard deviation is known to be 5 kN. You will take a sample of 100 cables and test H₀: μ = 500 kN against H₁: μ > 500 kN at α = 0.05. Above which sample mean x̄c will you reject H₀?

μ₀ = 500 kNσ = 5 kNn = 100α = 0.05
x̄c = kN
3.Medium
−2.1792.179t = ?df = 12

Two teaching methods are compared. Group 1: 5 students, mean score 47, standard deviation 12. Group 2: 9 students, mean score 60.4, standard deviation 7.5. 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 = 5x̄₁ = 47s₁ = 12n₂ = 9x̄₂ = 60.4s₂ = 7.5
t =
4.Medium
−2.1452.145t = ?df = 14

Two teaching methods are compared. Group 1: 10 students, mean score 64.5, standard deviation 2.5. Group 2: 6 students, mean score 75.4, standard deviation 10.5. 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 = 10x̄₁ = 64.5s₁ = 2.5n₂ = 6x̄₂ = 75.4s₂ = 10.5
t =
5.Hard
μ₀x̄c

A one-sided z test of H₀: μ = 100 against H₁: μ > 100 is done at α = 0.05 with a sample of 100; the standard deviation is known to be 5. In reality the mean is 101.15. Find the power 1 − β of the test in percent.

μ₀ = 100μ = 101.15σ = 5n = 100α = 0.05
1 − β = %
6.Hard
−1.961.96z = ?

In a trial, 80 of 200 patients on treatment A recover, and 100 of 200 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 80n₁ = 200x₂ = 100n₂ = 200
z =

Answer key

  1. 1. z = −1.8
  2. 2. x̄c = 500.8 kN
  3. 3. t = −2.598
  4. 4. t = −3.204
  5. 5. 1 − β = 74.38 %
  6. 6. z = −2.01

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