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
1.21p = ?

A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.21. Find the p-value p.

z = 1.21H₁: μ > μ₀
p =
2.Easy
μ₀x̄c = ?α = 0.10

A machine is set to fill packs with a mean of 200 g; you suspect it underfills. The standard deviation is known to be 8 g. You will weigh a sample of 16 packs and test H₀: μ = 200 against H₁: μ < 200 at α = 0.10. Below which sample mean x̄c will you reject H₀?

μ₀ = 200 gσ = 8 gn = 16α = 0.10
x̄c = g
3.Medium
t −2.0302.03

A sample of 36 students has a mean score of 76.6 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 76.6s = 8n = 36
t =
4.Medium
t −2.13102.131

A sample of 16 students has a mean score of 96.5 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 96.5s = 10n = 16
t =
5.Hard
σ = 15, 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 15. Find the smallest sample size n.

σ = 15E = 395%
n =
6.Hard
z −2.57602.576

A sample of 36 measurements has mean 49.8. The population standard deviation is 12. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 49.8σ = 12n = 3699%
L =

Answer key

  1. 1. p = 0.1131
  2. 2. x̄c = 197.4 g
  3. 3. t = 1.2
  4. 4. t = −1.4
  5. 5. n = 97
  6. 6. L = 44.65

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