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 120 mL on average. The standard deviation is known to be 5 mL. A sample of 100 bottles has a mean of 118.9 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 118.9 mLσ = 5 mLn = 100
z =
2.Easy
1.61p = ?

A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.61. Find the p-value p.

z = 1.61H₁: μ > μ₀
p =
3.Medium
t −2.13102.131

A sample of 16 students has a mean score of 118.3 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 118.3s = 5n = 16
t =
4.Medium
−2.04p = ?

The mean of a population is claimed to be 250; the population standard deviation is known to be 24. A random sample of 64 observations has a mean of 243.88. Test H₀: μ = 250 against H₁: μ < 250. Find the p-value p.

μ₀ = 250σ = 24n = 64x̄ = 243.88H₁: μ < μ₀
p =
5.Hard
z −2.57602.576

A sample of 81 measurements has mean 46.2. The population standard deviation is 15. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 46.2σ = 15n = 8199%
L =
6.Hard
−1.961.96z = ?

In a trial, 36 of 120 patients on treatment A recover, and 20 of 120 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 36n₁ = 120x₂ = 20n₂ = 120
z =

Answer key

  1. 1. z = −2.2
  2. 2. p = 0.0537
  3. 3. t = −1.36
  4. 4. p = 0.02068
  5. 5. L = 41.91
  6. 6. z = 2.442

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