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
μ₀x̄c = ?α = 0.05

A supplier claims that the mean breaking strength of a cable is 50 kN; you suspect it is higher. The standard deviation is known to be 5 kN. You will take a sample of 36 cables and test H₀: μ = 50 kN against H₁: μ > 50 kN at α = 0.05. Above which sample mean x̄c will you reject H₀?

μ₀ = 50 kNσ = 5 kNn = 36α = 0.05
x̄c = kN
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 8 mL. A sample of 16 bottles has a mean of 114.8 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 114.8 mLσ = 8 mLn = 16
z =
3.Medium
−1.961.96z = ?

Two production lines make the same part. Line 1: a sample of 50 parts has mean length 104 mm, and the line's known standard deviation is 16 mm. Line 2: a sample of 80 parts has mean 108.4 mm, known standard deviation 5 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 50x̄₁ = 104 mmσ₁ = 16 mmn₂ = 80x̄₂ = 108.4 mmσ₂ = 5 mm
z =
4.Medium
t −1.98401.984

A sample of 100 students has a mean score of 203.4 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 203.4s = 20n = 100
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 2.5α = 0.05βσ = 20, power 90%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 2.5 units with a power of 90%. The standard deviation is 20. Find the minimum sample size n.

α = 0.05power = 90%δ = 2.5σ = 20zα = 1.645zβ = 1.282
n =
6.Hard
z −2.57602.576

A sample of 64 measurements has mean 51.2. The population standard deviation is 12. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 51.2σ = 12n = 6499%
L =

Answer key

  1. 1. x̄c = 51.37 kN
  2. 2. z = −2.6
  3. 3. z = −1.888
  4. 4. t = 1.7
  5. 5. n = 549
  6. 6. L = 47.34

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