1.Easy
A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −0.98. Find the p-value p.
z = −0.98H₁: μ < μ₀
p =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 5 mL. A sample of 25 bottles has a mean of 49.1 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 49.1 mLσ = 5 mLn = 25
z =
3.Medium
Two production lines make the same part. Line 1: a sample of 40 parts has mean length 42 mm, and the line's known standard deviation is 17 mm. Line 2: a sample of 40 parts has mean 50.9 mm, known standard deviation 19 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 40x̄₁ = 42 mmσ₁ = 17 mmn₂ = 40x̄₂ = 50.9 mmσ₂ = 19 mm
z =
4.Medium
Two production lines make the same part. Line 1: a sample of 40 parts has mean length 116 mm, and the line's known standard deviation is 12 mm. Line 2: a sample of 50 parts has mean 120 mm, known standard deviation 15 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 40x̄₁ = 116 mmσ₁ = 12 mmn₂ = 50x̄₂ = 120 mmσ₂ = 15 mm
z =
5.Hard
A sample of 100 measurements has mean 51. The population standard deviation is 4. Find the lower limit L of the 95% confidence interval for the mean.
x̄ = 51σ = 4n = 10095%
L =
6.Hard
A one-sided z test at α = 0.05 must detect a shift of the mean of 1.5 units with a power of 95%. The standard deviation is 6. Find the minimum sample size n.
α = 0.05power = 95%δ = 1.5σ = 6zα = 1.645zβ = 1.645
n =
Answer key
- 1. p = 0.1635
- 2. z = −0.9
- 3. z = −2.208
- 4. z = −1.405
- 5. L = 50.22
- 6. n = 174
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