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 15 mL. A sample of 36 bottles has a mean of 506 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 506 mLσ = 15 mLn = 36
z =
2.Easy
−2.332.33p = ?

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = 2.33. Find the p-value p.

z = 2.33H₁: μ ≠ μ₀
p =
3.Medium
−2.2282.228t = ?df = 10

11 employees take a typing test before and after a training course. For each person the difference d = after − before (words per minute) is recorded. The mean difference is −1.9 and the standard deviation of the differences is 1.8. Find the paired test statistic t for H₀: μd = 0.

n = 11d̄ = −1.9sd = 1.8
t =
4.Medium
t −1.99801.998

A sample of 64 students has a mean score of 44.5 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 44.5s = 20n = 64
t =
5.Hard
−1.961.96z = ?

In a trial, 40 of 80 patients on treatment A recover, and 138 of 250 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 40n₁ = 80x₂ = 138n₂ = 250
z =
6.Hard
z −1.64501.645

A sample of 49 measurements has mean 498. The population standard deviation is 10. Find the lower limit L of the 90% confidence interval for the mean.

x̄ = 498σ = 10n = 4990%
L =

Answer key

  1. 1. z = 2.4
  2. 2. p = 0.01981
  3. 3. t = −3.501
  4. 4. t = −2.2
  5. 5. z = −0.8122
  6. 6. L = 495.6

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