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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Name: ____________________   Date: ____________

1.Easy
−1.9601.96z = ?

A company claims that a proportion of 0.25 of its customers are satisfied. In a random survey of 500 customers, 139 say they are satisfied. Find the test statistic z for H₀: p = 0.25.

p₀ = 0.25n = 500x = 139
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 15 mL. A sample of 25 bottles has a mean of 108.7 mL. Find the test statistic z for H₀: μ = 100.

μ₀ = 100 mLx̄ = 108.7 mLσ = 15 mLn = 25
z =
3.Medium
−1.961.96z = ?

Two production lines make the same part. Line 1: a sample of 40 parts has mean length 135 mm, and the line's known standard deviation is 8 mm. Line 2: a sample of 40 parts has mean 137.4 mm, known standard deviation 10 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 40x̄₁ = 135 mmσ₁ = 8 mmn₂ = 40x̄₂ = 137.4 mmσ₂ = 10 mm
z =
4.Medium
t −2.0302.03

A sample of 36 students has a mean score of 121.9 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 121.9s = 4n = 36
t =
5.Hard
σ = 15, n = ?x̄ − Ex̄ + Ex̄E = 0.599%

How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 0.5? The standard deviation is 15. Find the smallest sample size n.

σ = 15E = 0.599%
n =
6.Hard
H₀H₁μ₀x̄cμ₀ + 3α = 0.01βσ = 15, power 90%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 3 units with a power of 90%. The standard deviation is 15. Find the minimum sample size n.

α = 0.01power = 90%δ = 3σ = 15zα = 2.326zβ = 1.282
n =

Answer key

  1. 1. z = 1.446
  2. 2. z = 2.9
  3. 3. z = −1.185
  4. 4. t = 2.85
  5. 5. n = 5973
  6. 6. n = 326

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