1.Easy
A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 20 mL. A sample of 81 bottles has a mean of 71 mL. Find the test statistic z for H₀: μ = 75.
μ₀ = 75 mLx̄ = 71 mLσ = 20 mLn = 81
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 8 mL. A sample of 100 bottles has a mean of 99.28 mL. Find the test statistic z for H₀: μ = 100.
μ₀ = 100 mLx̄ = 99.28 mLσ = 8 mLn = 100
z =
3.Medium
Two production lines make the same part. Line 1: a sample of 50 parts has mean length 60.5 mm, and the line's known standard deviation is 14 mm. Line 2: a sample of 40 parts has mean 56.6 mm, known standard deviation 14 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 50x̄₁ = 60.5 mmσ₁ = 14 mmn₂ = 40x̄₂ = 56.6 mmσ₂ = 14 mm
z =
4.Medium
Two production lines make the same part. Line 1: a sample of 80 parts has mean length 59 mm, and the line's known standard deviation is 6 mm. Line 2: a sample of 60 parts has mean 57.3 mm, known standard deviation 14 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 80x̄₁ = 59 mmσ₁ = 6 mmn₂ = 60x̄₂ = 57.3 mmσ₂ = 14 mm
z =
5.Hard
In a trial, 90 of 300 patients on treatment A recover, and 18 of 80 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 90n₁ = 300x₂ = 18n₂ = 80
z =
6.Hard
A sample of 64 measurements has mean 101.3. The population standard deviation is 4. Find the upper limit U of the 95% confidence interval for the mean.
x̄ = 101.3σ = 4n = 6495%
U =
Answer key
- 1. z = −1.8
- 2. z = −0.9
- 3. z = 1.313
- 4. z = 0.8818
- 5. z = 1.321
- 6. U = 102.3
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