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 100 mL on average. The standard deviation is known to be 4 mL. A sample of 16 bottles has a mean of 101.2 mL. Find the test statistic z for H₀: μ = 100.

μ₀ = 100 mLx̄ = 101.2 mLσ = 4 mLn = 16
z =
2.Easy
μ₀x̄c = ?α = 0.05

A machine is set to fill packs with a mean of 100 g; you suspect it underfills. The standard deviation is known to be 10 g. You will weigh a sample of 25 packs and test H₀: μ = 100 against H₁: μ < 100 at α = 0.05. Below which sample mean x̄c will you reject H₀?

μ₀ = 100 gσ = 10 gn = 25α = 0.05
x̄c = g
3.Medium
t −1.98401.984

A sample of 100 students has a mean score of 121.4 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 121.4s = 8n = 100
t =
4.Medium
t −2.0302.03

A sample of 36 students has a mean score of 503.2 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 503.2s = 8n = 36
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 2α = 0.05βσ = 17, power 95%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 2 units with a power of 95%. The standard deviation is 17. Find the minimum sample size n.

α = 0.05power = 95%δ = 2σ = 17zα = 1.645zβ = 1.645
n =
6.Hard
H₀H₁μ₀x̄cμ₀ + 1.5α = 0.01βσ = 4, power 90%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 1.5 units with a power of 90%. The standard deviation is 4. Find the minimum sample size n.

α = 0.01power = 90%δ = 1.5σ = 4zα = 2.326zβ = 1.282
n =

Answer key

  1. 1. z = 1.2
  2. 2. x̄c = 96.71 g
  3. 3. t = 1.75
  4. 4. t = 2.4
  5. 5. n = 783
  6. 6. n = 93

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