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
1.99p = ?

A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.99. Find the p-value p.

z = 1.99H₁: μ > μ₀
p =
2.Easy
−1.9601.96z = ?

A company claims that a proportion of 0.3 of its customers are satisfied. In a random survey of 120 customers, 31 say they are satisfied. Find the test statistic z for H₀: p = 0.3.

p₀ = 0.3n = 120x = 31
z =
3.Medium
−1.961.96z = ?

Two production lines make the same part. Line 1: a sample of 50 parts has mean length 89.5 mm, and the line's known standard deviation is 13 mm. Line 2: a sample of 50 parts has mean 82.2 mm, known standard deviation 14 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 50x̄₁ = 89.5 mmσ₁ = 13 mmn₂ = 50x̄₂ = 82.2 mmσ₂ = 14 mm
z =
4.Medium
t −2.0302.03

A sample of 36 students has a mean score of 67.67 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 67.67s = 20n = 36
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 4α = 0.05βσ = 26, power 80%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 4 units with a power of 80%. The standard deviation is 26. Find the minimum sample size n.

α = 0.05power = 80%δ = 4σ = 26zα = 1.645zβ = 0.842
n =
6.Hard
z −2.57602.576

A sample of 25 measurements has mean 50.6. The population standard deviation is 8. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 50.6σ = 8n = 2599%
L =

Answer key

  1. 1. p = 0.0233
  2. 2. z = −0.996
  3. 3. z = 2.702
  4. 4. t = −2.199
  5. 5. n = 262
  6. 6. L = 46.48

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