1.Easy
A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 15 mL. A sample of 64 bottles has a mean of 96.63 mL. Find the test statistic z for H₀: μ = 100.
μ₀ = 100 mLx̄ = 96.63 mLσ = 15 mLn = 64
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 15 mL. A sample of 16 bottles has a mean of 108.4 mL. Find the test statistic z for H₀: μ = 120.
μ₀ = 120 mLx̄ = 108.4 mLσ = 15 mLn = 16
z =
3.Medium
Two production lines make the same part. Line 1: a sample of 30 parts has mean length 129.5 mm, and the line's known standard deviation is 10 mm. Line 2: a sample of 30 parts has mean 122 mm, known standard deviation 18 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 30x̄₁ = 129.5 mmσ₁ = 10 mmn₂ = 30x̄₂ = 122 mmσ₂ = 18 mm
z =
4.Medium
Two production lines make the same part. Line 1: a sample of 40 parts has mean length 132 mm, and the line's known standard deviation is 10 mm. Line 2: a sample of 30 parts has mean 135.2 mm, known standard deviation 12 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 40x̄₁ = 132 mmσ₁ = 10 mmn₂ = 30x̄₂ = 135.2 mmσ₂ = 12 mm
z =
5.Hard
A sample of 25 measurements has mean 81.8. The population standard deviation is 20. Find the upper limit U of the 99% confidence interval for the mean.
x̄ = 81.8σ = 20n = 2599%
U =
6.Hard
A one-sided z test of H₀: μ = 200 against H₁: μ < 200 is done at α = 0.05 with a sample of 36; the standard deviation is known to be 12. In reality the mean is 194.6. Find the probability of a Type II error β in percent.
μ₀ = 200μ = 194.6σ = 12n = 36α = 0.05
β = %
Answer key
- 1. z = −1.797
- 2. z = −3.093
- 3. z = 1.995
- 4. z = −1.184
- 5. U = 92.1
- 6. β = 14.57 %
Full step-by-step solutions: practise this topic on examproblems.com.