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 12 mL. A sample of 100 bottles has a mean of 73.32 mL. Find the test statistic z for H₀: μ = 75.

μ₀ = 75 mLx̄ = 73.32 mLσ = 12 mLn = 100
z =
2.Easy
μ₀x̄c = ?α = 0.10

A supplier claims that the mean breaking strength of a cable is 200 kN; you suspect it is higher. The standard deviation is known to be 8 kN. You will take a sample of 36 cables and test H₀: μ = 200 kN against H₁: μ > 200 kN at α = 0.10. Above which sample mean x̄c will you reject H₀?

μ₀ = 200 kNσ = 8 kNn = 36α = 0.10
x̄c = kN
3.Medium
t −1.9901.99

A sample of 81 students has a mean score of 201.1 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 201.1s = 8n = 81
t =
4.Medium
t −1.98401.984

A sample of 100 students has a mean score of 201.1 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 201.1s = 15n = 100
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 2α = 0.01βσ = 10, power 80%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 2 units with a power of 80%. The standard deviation is 10. Find the minimum sample size n.

α = 0.01power = 80%δ = 2σ = 10zα = 2.326zβ = 0.842
n =
6.Hard
z −1.64501.645

A sample of 25 measurements has mean 504.8. The population standard deviation is 8. Find the upper limit U of the 90% confidence interval for the mean.

x̄ = 504.8σ = 8n = 2590%
U =

Answer key

  1. 1. z = −1.4
  2. 2. x̄c = 201.7 kN
  3. 3. t = 1.237
  4. 4. t = 0.7333
  5. 5. n = 251
  6. 6. U = 507.4

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