1.Easy
A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −1.63. Find the p-value p.
z = −1.63H₁: μ < μ₀
p =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A supplier claims that the mean breaking strength of a cable is 100 kN; you suspect it is higher. The standard deviation is known to be 3 kN. You will take a sample of 36 cables and test H₀: μ = 100 kN against H₁: μ > 100 kN at α = 0.05. Above which sample mean x̄c will you reject H₀?
μ₀ = 100 kNσ = 3 kNn = 36α = 0.05
x̄c = kN
3.Medium
Two production lines make the same part. Line 1: a sample of 100 parts has mean length 106 mm, and the line's known standard deviation is 12 mm. Line 2: a sample of 40 parts has mean 109.9 mm, known standard deviation 4 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 100x̄₁ = 106 mmσ₁ = 12 mmn₂ = 40x̄₂ = 109.9 mmσ₂ = 4 mm
z =
4.Medium
A sample of 81 students has a mean score of 200.8 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 200.
μ₀ = 200x̄ = 200.8s = 4n = 81
t =
5.Hard
How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 1? The standard deviation is 8. Find the smallest sample size n.
σ = 8E = 195%
n =
6.Hard
A sample of 36 measurements has mean 42.8. The population standard deviation is 15. Find the upper limit U of the 99% confidence interval for the mean.
x̄ = 42.8σ = 15n = 3699%
U =
Answer key
- 1. p = 0.05155
- 2. x̄c = 100.8 kN
- 3. z = −2.875
- 4. t = 1.8
- 5. n = 246
- 6. U = 49.24
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