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 50 mL on average. The standard deviation is known to be 4 mL. A sample of 25 bottles has a mean of 47.92 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 47.92 mLσ = 4 mLn = 25
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 8 mL. A sample of 81 bottles has a mean of 122.6 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 122.6 mLσ = 8 mLn = 81
z =
3.Medium
−2.1792.179t = ?df = 12

13 employees take a typing test before and after a training course. For each person the difference d = after − before (words per minute) is recorded. The mean difference is 6.82 and the standard deviation of the differences is 8.2. Find the paired test statistic t for H₀: μd = 0.

n = 13d̄ = 6.82sd = 8.2
t =
4.Medium
−2.0642.064t = ?df = 24

Two teaching methods are compared. Group 1: 13 students, mean score 84, standard deviation 2. Group 2: 13 students, mean score 90.2, standard deviation 8. 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 = 84s₁ = 2n₂ = 13x̄₂ = 90.2s₂ = 8
t =
5.Hard
−1.961.96z = ?

In a trial, 45 of 150 patients on treatment A recover, and 57 of 300 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 45n₁ = 150x₂ = 57n₂ = 300
z =
6.Hard
H₀H₁μ₀x̄cμ₀ + 3α = 0.05βσ = 26, power 90%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 3 units with a power of 90%. The standard deviation is 26. Find the minimum sample size n.

α = 0.05power = 90%δ = 3σ = 26zα = 1.645zβ = 1.282
n =

Answer key

  1. 1. z = −2.6
  2. 2. z = 2.925
  3. 3. t = 2.999
  4. 4. t = −2.711
  5. 5. z = 2.627
  6. 6. n = 644

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