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 8 mL. A sample of 25 bottles has a mean of 503.8 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 503.8 mLσ = 8 mLn = 25
z =
2.Easy
−0.970.97p = ?

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = 0.97. Find the p-value p.

z = 0.97H₁: μ ≠ μ₀
p =
3.Medium
−1.981.98p = ?

The mean of a population is claimed to be 100; the population standard deviation is known to be 7.5. A random sample of 25 observations has a mean of 97.03. Test H₀: μ = 100 against H₁: μ ≠ 100. Find the p-value p.

μ₀ = 100σ = 7.5n = 25x̄ = 97.03H₁: μ ≠ μ₀
p =
4.Medium
t −2.13102.131

A sample of 16 students has a mean score of 57.25 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 57.25s = 10n = 16
t =
5.Hard
σ = 5, n = ?x̄ − Ex̄ + Ex̄E = 399%

How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 3? The standard deviation is 5. Find the smallest sample size n.

σ = 5E = 399%
n =
6.Hard
−1.961.96z = ?

In a trial, 90 of 150 patients on treatment A recover, and 65 of 100 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 90n₁ = 150x₂ = 65n₂ = 100
z =

Answer key

  1. 1. z = 2.375
  2. 2. p = 0.332
  3. 3. p = 0.0477
  4. 4. t = 2.9
  5. 5. n = 19
  6. 6. z = −0.7979

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