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 8 mL. A sample of 16 bottles has a mean of 124.2 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 124.2 mLσ = 8 mLn = 16
z =
2.Easy
−2.13p = ?

A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −2.13. Find the p-value p.

z = −2.13H₁: μ < μ₀
p =
3.Medium
t −1.98401.984

A sample of 100 students has a mean score of 118.9 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 118.9s = 12n = 100
t =
4.Medium
t −2.0302.03

A sample of 36 students has a mean score of 101 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 101s = 5n = 36
t =
5.Hard
σ = 12, n = ?x̄ − Ex̄ + Ex̄E = 395%

How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 3? The standard deviation is 12. Find the smallest sample size n.

σ = 12E = 395%
n =
6.Hard
H₀H₁μ₀x̄cμ₀ + 3α = 0.05βσ = 28, power 90%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 3 units with a power of 90%. The standard deviation is 28. Find the minimum sample size n.

α = 0.05power = 90%δ = 3σ = 28zα = 1.645zβ = 1.282
n =

Answer key

  1. 1. z = 2.1
  2. 2. p = 0.01659
  3. 3. t = −0.9167
  4. 4. t = 1.2
  5. 5. n = 62
  6. 6. n = 747

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