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 100 mL on average. The standard deviation is known to be 15 mL. A sample of 49 bottles has a mean of 96.14 mL. Find the test statistic z for H₀: μ = 100.

μ₀ = 100 mLx̄ = 96.14 mLσ = 15 mLn = 49
z =
2.Easy
−1.9601.96z = ?

A company claims that a proportion of 0.6 of its customers are satisfied. In a random survey of 120 customers, 85 say they are satisfied. Find the test statistic z for H₀: p = 0.6.

p₀ = 0.6n = 120x = 85
z =
3.Medium
−1.36p = ?

The mean of a population is claimed to be 100; the population standard deviation is known to be 25. A random sample of 100 observations has a mean of 96.6. Test H₀: μ = 100 against H₁: μ < 100. Find the p-value p.

μ₀ = 100σ = 25n = 100x̄ = 96.6H₁: μ < μ₀
p =
4.Medium
1.94p = ?

The mean of a population is claimed to be 50; the population standard deviation is known to be 2.5. A random sample of 25 observations has a mean of 50.97. Test H₀: μ = 50 against H₁: μ > 50. Find the p-value p.

μ₀ = 50σ = 2.5n = 25x̄ = 50.97H₁: μ > μ₀
p =
5.Hard
z −1.64501.645

A sample of 16 measurements has mean 211.3. The population standard deviation is 15. Find the upper limit U of the 90% confidence interval for the mean.

x̄ = 211.3σ = 15n = 1690%
U =
6.Hard
H₀H₁μ₀x̄cμ₀ + 3α = 0.05βσ = 18, power 95%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 3 units with a power of 95%. The standard deviation is 18. Find the minimum sample size n.

α = 0.05power = 95%δ = 3σ = 18zα = 1.645zβ = 1.645
n =

Answer key

  1. 1. z = −1.801
  2. 2. z = 2.422
  3. 3. p = 0.08692
  4. 4. p = 0.02619
  5. 5. U = 217.5
  6. 6. n = 390

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