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 50 mL on average. The standard deviation is known to be 15 mL. A sample of 16 bottles has a mean of 60.88 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 60.88 mLσ = 15 mLn = 16
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 8 mL. A sample of 64 bottles has a mean of 498.2 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 498.2 mLσ = 8 mLn = 64
z =
3.Medium
t −2.06402.064

A sample of 25 students has a mean score of 496.4 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 496.4s = 20n = 25
t =
4.Medium
t −1.9901.99

A sample of 81 students has a mean score of 115.9 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 115.9s = 12n = 81
t =
5.Hard
−1.961.96z = ?

In a trial, 195 of 300 patients on treatment A recover, and 130 of 250 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 195n₁ = 300x₂ = 130n₂ = 250
z =
6.Hard
z −2.57602.576

A sample of 100 measurements has mean 502.5. The population standard deviation is 12. Find the upper limit U of the 99% confidence interval for the mean.

x̄ = 502.5σ = 12n = 10099%
U =

Answer key

  1. 1. z = 2.901
  2. 2. z = −1.8
  3. 3. t = −0.9
  4. 4. t = −3.075
  5. 5. z = 3.088
  6. 6. U = 505.6

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