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 500 mL on average. The standard deviation is known to be 10 mL. A sample of 81 bottles has a mean of 501.3 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 501.3 mLσ = 10 mLn = 81
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 5 mL. A sample of 49 bottles has a mean of 200.9 mL. Find the test statistic z for H₀: μ = 200.

μ₀ = 200 mLx̄ = 200.9 mLσ = 5 mLn = 49
z =
3.Medium
t −2.06402.064

A sample of 25 students has a mean score of 202.4 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 202.4s = 10n = 25
t =
4.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 −1.02 and the standard deviation of the differences is 2.2. Find the paired test statistic t for H₀: μd = 0.

n = 12d̄ = −1.02sd = 2.2
t =
5.Hard
−1.961.96z = ?

In a trial, 98 of 150 patients on treatment A recover, and 188 of 250 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 98n₁ = 150x₂ = 188n₂ = 250
z =
6.Hard
H₀H₁μ₀x̄cμ₀ + 2α = 0.05βσ = 7, power 95%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 2 units with a power of 95%. The standard deviation is 7. Find the minimum sample size n.

α = 0.05power = 95%δ = 2σ = 7zα = 1.645zβ = 1.645
n =

Answer key

  1. 1. z = 1.17
  2. 2. z = 1.26
  3. 3. t = 1.2
  4. 4. t = −1.606
  5. 5. z = −2.116
  6. 6. n = 133

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