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 500 mL on average. The standard deviation is known to be 4 mL. A sample of 16 bottles has a mean of 498.2 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 498.2 mLσ = 4 mLn = 16
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 10 mL. A sample of 16 bottles has a mean of 56 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 56 mLσ = 10 mLn = 16
z =
3.Medium
t −2.13102.131

A sample of 16 students has a mean score of 196.5 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 196.5s = 10n = 16
t =
4.Medium
1.24p = ?

The mean of a population is claimed to be 100; the population standard deviation is known to be 12. A random sample of 144 observations has a mean of 101.24. Test H₀: μ = 100 against H₁: μ > 100. Find the p-value p.

μ₀ = 100σ = 12n = 144x̄ = 101.24H₁: μ > μ₀
p =
5.Hard
H₀H₁μ₀x̄cμ₀ + 4α = 0.01βσ = 21, power 90%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 4 units with a power of 90%. The standard deviation is 21. Find the minimum sample size n.

α = 0.01power = 90%δ = 4σ = 21zα = 2.326zβ = 1.282
n =
6.Hard
H₀H₁μ₀x̄cμ₀ + 2.5α = 0.01βσ = 6, power 95%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 2.5 units with a power of 95%. The standard deviation is 6. Find the minimum sample size n.

α = 0.01power = 95%δ = 2.5σ = 6zα = 2.326zβ = 1.645
n =

Answer key

  1. 1. z = −1.8
  2. 2. z = 2.4
  3. 3. t = −1.4
  4. 4. p = 0.1075
  5. 5. n = 359
  6. 6. n = 91

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