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
1.81p = ?

A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.81. Find the p-value p.

z = 1.81H₁: μ > μ₀
p =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 5 mL. A sample of 81 bottles has a mean of 199.2 mL. Find the test statistic z for H₀: μ = 200.

μ₀ = 200 mLx̄ = 199.2 mLσ = 5 mLn = 81
z =
3.Medium
−2.0862.086t = ?df = 20

Two teaching methods are compared. Group 1: 5 students, mean score 37.5, standard deviation 6.5. Group 2: 17 students, mean score 32.7, standard deviation 7.5. Assume equal population variances and use the pooled two-sample t test. Find the test statistic t for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (group 1 minus group 2).

n₁ = 5x̄₁ = 37.5s₁ = 6.5n₂ = 17x̄₂ = 32.7s₂ = 7.5
t =
4.Medium
−0.980.98p = ?

The mean of a population is claimed to be 100; the population standard deviation is known to be 18. A random sample of 144 observations has a mean of 101.47. Test H₀: μ = 100 against H₁: μ ≠ 100. Find the p-value p.

μ₀ = 100σ = 18n = 144x̄ = 101.47H₁: μ ≠ μ₀
p =
5.Hard
−1.961.96z = ?

In a trial, 63 of 250 patients on treatment A recover, and 73 of 250 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 63n₁ = 250x₂ = 73n₂ = 250
z =
6.Hard
H₀H₁μ₀x̄cμ₀ + 4α = 0.01βσ = 20, power 90%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 4 units with a power of 90%. The standard deviation is 20. Find the minimum sample size n.

α = 0.01power = 90%δ = 4σ = 20zα = 2.326zβ = 1.282
n =

Answer key

  1. 1. p = 0.03515
  2. 2. z = −1.44
  3. 3. t = 1.291
  4. 4. p = 0.3271
  5. 5. z = −1.005
  6. 6. n = 326

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