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 10 mL. A sample of 64 bottles has a mean of 46.13 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 46.13 mLσ = 10 mLn = 64
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 5 mL. A sample of 100 bottles has a mean of 50.85 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 50.85 mLσ = 5 mLn = 100
z =
3.Medium
t −1.99801.998

A sample of 64 students has a mean score of 198.4 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 198.4s = 5n = 64
t =
4.Medium
−2.3062.306t = ?df = 8

9 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 3.6 and the standard deviation of the differences is 7.2. Find the paired test statistic t for H₀: μd = 0.

n = 9d̄ = 3.6sd = 7.2
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 1.5α = 0.05βσ = 11, power 95%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 1.5 units with a power of 95%. The standard deviation is 11. Find the minimum sample size n.

α = 0.05power = 95%δ = 1.5σ = 11zα = 1.645zβ = 1.645
n =
6.Hard
z −1.9601.96

A sample of 81 measurements has mean 97.3. The population standard deviation is 12. Find the upper limit U of the 95% confidence interval for the mean.

x̄ = 97.3σ = 12n = 8195%
U =

Answer key

  1. 1. z = −3.096
  2. 2. z = 1.7
  3. 3. t = −2.56
  4. 4. t = 1.5
  5. 5. n = 583
  6. 6. U = 99.91

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