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
−1.36p = ?

A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −1.36. Find the p-value p.

z = −1.36H₁: μ < μ₀
p =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 20 mL. A sample of 49 bottles has a mean of 103.4 mL. Find the test statistic z for H₀: μ = 100.

μ₀ = 100 mLx̄ = 103.4 mLσ = 20 mLn = 49
z =
3.Medium
−2.182.18p = ?

The mean of a population is claimed to be 120; the population standard deviation is known to be 12. A random sample of 36 observations has a mean of 124.36. Test H₀: μ = 120 against H₁: μ ≠ 120. Find the p-value p.

μ₀ = 120σ = 12n = 36x̄ = 124.36H₁: μ ≠ μ₀
p =
4.Medium
t −1.99801.998

A sample of 64 students has a mean score of 496.6 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 496.6s = 15n = 64
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 3α = 0.05βσ = 8, power 95%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 3 units with a power of 95%. The standard deviation is 8. Find the minimum sample size n.

α = 0.05power = 95%δ = 3σ = 8zα = 1.645zβ = 1.645
n =
6.Hard
z −1.64501.645

A sample of 100 measurements has mean 118.8. The population standard deviation is 5. Find the lower limit L of the 90% confidence interval for the mean.

x̄ = 118.8σ = 5n = 10090%
L =

Answer key

  1. 1. p = 0.08692
  2. 2. z = 1.19
  3. 3. p = 0.02926
  4. 4. t = −1.813
  5. 5. n = 77
  6. 6. L = 118

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