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 5 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 = 5 mLn = 81
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 4 mL. A sample of 64 bottles has a mean of 121 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 121 mLσ = 4 mLn = 64
z =
3.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 −4.71 and the standard deviation of the differences is 6.8. Find the paired test statistic t for H₀: μd = 0.

n = 12d̄ = −4.71sd = 6.8
t =
4.Medium
1.94p = ?

The mean of a population is claimed to be 250; the population standard deviation is known to be 12. A random sample of 64 observations has a mean of 252.91. Test H₀: μ = 250 against H₁: μ > 250. Find the p-value p.

μ₀ = 250σ = 12n = 64x̄ = 252.91H₁: μ > μ₀
p =
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
σ = 10, n = ?x̄ − Ex̄ + Ex̄E = 0.595%

How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 0.5? The standard deviation is 10. Find the smallest sample size n.

σ = 10E = 0.595%
n =

Answer key

  1. 1. z = 2.34
  2. 2. z = 2
  3. 3. t = −2.399
  4. 4. p = 0.02619
  5. 5. n = 62
  6. 6. n = 1537

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