1.Easy
A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 20 mL. A sample of 100 bottles has a mean of 96.4 mL. Find the test statistic z for H₀: μ = 100.
μ₀ = 100 mLx̄ = 96.4 mLσ = 20 mLn = 100
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 15 mL. A sample of 36 bottles has a mean of 207.3 mL. Find the test statistic z for H₀: μ = 200.
μ₀ = 200 mLx̄ = 207.3 mLσ = 15 mLn = 36
z =
3.Medium
A sample of 81 students has a mean score of 121.2 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 120.
μ₀ = 120x̄ = 121.2s = 15n = 81
t =
4.Medium
Two production lines make the same part. Line 1: a sample of 30 parts has mean length 68.5 mm, and the line's known standard deviation is 7 mm. Line 2: a sample of 40 parts has mean 70.1 mm, known standard deviation 8 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 30x̄₁ = 68.5 mmσ₁ = 7 mmn₂ = 40x̄₂ = 70.1 mmσ₂ = 8 mm
z =
5.Hard
A one-sided z test at α = 0.05 must detect a shift of the mean of 5 units with a power of 90%. The standard deviation is 11. Find the minimum sample size n.
α = 0.05power = 90%δ = 5σ = 11zα = 1.645zβ = 1.282
n =
6.Hard
A sample of 100 measurements has mean 51.9. The population standard deviation is 12. Find the lower limit L of the 90% confidence interval for the mean.
x̄ = 51.9σ = 12n = 10090%
L =
Answer key
- 1. z = −1.8
- 2. z = 2.92
- 3. t = 0.72
- 4. z = −0.8898
- 5. n = 42
- 6. L = 49.93
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