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 75 mL on average. The standard deviation is known to be 8 mL. A sample of 64 bottles has a mean of 73.6 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 73.6 mLσ = 8 mLn = 64
z =
2.Easy
0.89p = ?

A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 0.89. Find the p-value p.

z = 0.89H₁: μ > μ₀
p =
3.Medium
t −2.01102.011

A sample of 49 students has a mean score of 102.6 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 102.6s = 15n = 49
t =
4.Medium
−2.1792.179t = ?df = 12

13 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 2.53 and the standard deviation of the differences is 3.8. Find the paired test statistic t for H₀: μd = 0.

n = 13d̄ = 2.53sd = 3.8
t =
5.Hard
σ = 10, n = ?x̄ − Ex̄ + Ex̄E = 195%

How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 1? The standard deviation is 10. Find the smallest sample size n.

σ = 10E = 195%
n =
6.Hard
z −1.64501.645

A sample of 36 measurements has mean 97.7. The population standard deviation is 10. Find the upper limit U of the 90% confidence interval for the mean.

x̄ = 97.7σ = 10n = 3690%
U =

Answer key

  1. 1. z = −1.4
  2. 2. p = 0.1867
  3. 3. t = 1.213
  4. 4. t = 2.401
  5. 5. n = 385
  6. 6. U = 100.4

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