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 120 mL on average. The standard deviation is known to be 12 mL. A sample of 36 bottles has a mean of 125.8 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 125.8 mLσ = 12 mLn = 36
z =
2.Easy
−1.9601.96z = ?

A company claims that a proportion of 0.6 of its customers are satisfied. In a random survey of 200 customers, 135 say they are satisfied. Find the test statistic z for H₀: p = 0.6.

p₀ = 0.6n = 200x = 135
z =
3.Medium
t −2.06402.064

A sample of 25 students has a mean score of 119.3 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 119.3s = 4n = 25
t =
4.Medium
t −1.9901.99

A sample of 81 students has a mean score of 506.4 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 506.4s = 20n = 81
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 5α = 0.01βσ = 12, power 80%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 5 units with a power of 80%. The standard deviation is 12. Find the minimum sample size n.

α = 0.01power = 80%δ = 5σ = 12zα = 2.326zβ = 0.842
n =
6.Hard
H₀H₁μ₀x̄cμ₀ + 4α = 0.01βσ = 23, power 95%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 4 units with a power of 95%. The standard deviation is 23. Find the minimum sample size n.

α = 0.01power = 95%δ = 4σ = 23zα = 2.326zβ = 1.645
n =

Answer key

  1. 1. z = 2.9
  2. 2. z = 2.165
  3. 3. t = −0.875
  4. 4. t = 2.88
  5. 5. n = 58
  6. 6. n = 522

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