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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Name: ____________________   Date: ____________

1.Easy
−1.9601.96z = ?

A company claims that a proportion of 0.2 of its customers are satisfied. In a random survey of 120 customers, 13 say they are satisfied. Find the test statistic z for H₀: p = 0.2.

p₀ = 0.2n = 120x = 13
z =
2.Easy
−0.90.9p = ?

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = 0.9. Find the p-value p.

z = 0.9H₁: μ ≠ μ₀
p =
3.Medium
−2.2012.201t = ?df = 11

12 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 2.34 and the standard deviation of the differences is 8.1. Find the paired test statistic t for H₀: μd = 0.

n = 12d̄ = 2.34sd = 8.1
t =
4.Medium
−2.1792.179t = ?df = 12

Two teaching methods are compared. Group 1: 5 students, mean score 27, standard deviation 7.5. Group 2: 9 students, mean score 22.9, standard deviation 4.5. 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 = 27s₁ = 7.5n₂ = 9x̄₂ = 22.9s₂ = 4.5
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 3α = 0.05βσ = 25, power 80%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 3 units with a power of 80%. The standard deviation is 25. Find the minimum sample size n.

α = 0.05power = 80%δ = 3σ = 25zα = 1.645zβ = 0.842
n =
6.Hard
H₀H₁μ₀x̄cμ₀ + 4α = 0.01βσ = 10, power 80%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 4 units with a power of 80%. The standard deviation is 10. Find the minimum sample size n.

α = 0.01power = 80%δ = 4σ = 10zα = 2.326zβ = 0.842
n =

Answer key

  1. 1. z = −2.51
  2. 2. p = 0.3681
  3. 3. t = 1.001
  4. 4. t = 1.294
  5. 5. n = 430
  6. 6. n = 63

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