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
−1.9601.96z = ?

A company claims that a proportion of 0.25 of its customers are satisfied. In a random survey of 250 customers, 81 say they are satisfied. Find the test statistic z for H₀: p = 0.25.

p₀ = 0.25n = 250x = 81
z =
2.Easy
μ₀x̄c = ?α = 0.10

A supplier claims that the mean breaking strength of a cable is 50 kN; you suspect it is higher. The standard deviation is known to be 8 kN. You will take a sample of 64 cables and test H₀: μ = 50 kN against H₁: μ > 50 kN at α = 0.10. Above which sample mean x̄c will you reject H₀?

μ₀ = 50 kNσ = 8 kNn = 64α = 0.10
x̄c = kN
3.Medium
t −2.13102.131

A sample of 16 students has a mean score of 123.5 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 123.5s = 20n = 16
t =
4.Medium
−1.961.96z = ?

Two production lines make the same part. Line 1: a sample of 50 parts has mean length 59.5 mm, and the line's known standard deviation is 19 mm. Line 2: a sample of 40 parts has mean 55.7 mm, known standard deviation 11 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 50x̄₁ = 59.5 mmσ₁ = 19 mmn₂ = 40x̄₂ = 55.7 mmσ₂ = 11 mm
z =
5.Hard
z −1.64501.645

A sample of 49 measurements has mean 201.1. The population standard deviation is 8. Find the lower limit L of the 90% confidence interval for the mean.

x̄ = 201.1σ = 8n = 4990%
L =
6.Hard
H₀H₁μ₀x̄cμ₀ + 3α = 0.05βσ = 19, 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 19. Find the minimum sample size n.

α = 0.05power = 90%δ = 3σ = 19zα = 1.645zβ = 1.282
n =

Answer key

  1. 1. z = 2.702
  2. 2. x̄c = 51.28 kN
  3. 3. t = 0.7
  4. 4. z = 1.187
  5. 5. L = 199.2
  6. 6. n = 344

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