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 15 mL. A sample of 36 bottles has a mean of 117.8 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 117.8 mLσ = 15 mLn = 36
z =
2.Easy
−2.34p = ?

A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −2.34. Find the p-value p.

z = −2.34H₁: μ < μ₀
p =
3.Medium
−2.3652.365t = ?df = 7

8 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 6.49 and the standard deviation of the differences is 10.2. Find the paired test statistic t for H₀: μd = 0.

n = 8d̄ = 6.49sd = 10.2
t =
4.Medium
t −1.99801.998

A sample of 64 students has a mean score of 78 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 78s = 20n = 64
t =
5.Hard
−1.961.96z = ?

In a trial, 40 of 200 patients on treatment A recover, and 24 of 200 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 40n₁ = 200x₂ = 24n₂ = 200
z =
6.Hard
H₀H₁μ₀x̄cμ₀ + 5α = 0.01βσ = 20, power 95%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 5 units with a power of 95%. The standard deviation is 20. Find the minimum sample size n.

α = 0.01power = 95%δ = 5σ = 20zα = 2.326zβ = 1.645
n =

Answer key

  1. 1. z = −0.88
  2. 2. p = 0.009642
  3. 3. t = 1.8
  4. 4. t = 1.2
  5. 5. z = 2.182
  6. 6. n = 253

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