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
−1.871.87p = ?

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = −1.87. Find the p-value p.

z = −1.87H₁: μ ≠ μ₀
p =
2.Easy
μ₀x̄c = ?α = 0.10

A machine is set to fill packs with a mean of 100 g; you suspect it underfills. The standard deviation is known to be 4 g. You will weigh a sample of 64 packs and test H₀: μ = 100 against H₁: μ < 100 at α = 0.10. Below which sample mean x̄c will you reject H₀?

μ₀ = 100 gσ = 4 gn = 64α = 0.10
x̄c = g
3.Medium
t −2.06402.064

A sample of 25 students has a mean score of 47.2 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 47.2s = 10n = 25
t =
4.Medium
−1.961.96z = ?

Two production lines make the same part. Line 1: a sample of 30 parts has mean length 63.5 mm, and the line's known standard deviation is 6 mm. Line 2: a sample of 80 parts has mean 58.2 mm, known standard deviation 18 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 30x̄₁ = 63.5 mmσ₁ = 6 mmn₂ = 80x̄₂ = 58.2 mmσ₂ = 18 mm
z =
5.Hard
H₀H₁μ₀x̄cμ₀ + 3α = 0.05βσ = 15, power 80%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 3 units with a power of 80%. The standard deviation is 15. Find the minimum sample size n.

α = 0.05power = 80%δ = 3σ = 15zα = 1.645zβ = 0.842
n =
6.Hard
z −1.9601.96

A sample of 100 measurements has mean 205. The population standard deviation is 20. Find the lower limit L of the 95% confidence interval for the mean.

x̄ = 205σ = 20n = 10095%
L =

Answer key

  1. 1. p = 0.06148
  2. 2. x̄c = 99.36 g
  3. 3. t = −1.4
  4. 4. z = 2.313
  5. 5. n = 155
  6. 6. L = 201.1

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