1.Easy
A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −1.48. Find the p-value p.
z = −1.48H₁: μ < μ₀
p =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 4 mL. A sample of 100 bottles has a mean of 74.28 mL. Find the test statistic z for H₀: μ = 75.
μ₀ = 75 mLx̄ = 74.28 mLσ = 4 mLn = 100
z =
3.Medium
Two production lines make the same part. Line 1: a sample of 40 parts has mean length 109 mm, and the line's known standard deviation is 6 mm. Line 2: a sample of 80 parts has mean 106.9 mm, known standard deviation 7 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 40x̄₁ = 109 mmσ₁ = 6 mmn₂ = 80x̄₂ = 106.9 mmσ₂ = 7 mm
z =
4.Medium
Two production lines make the same part. Line 1: a sample of 100 parts has mean length 109.5 mm, and the line's known standard deviation is 3 mm. Line 2: a sample of 40 parts has mean 108.6 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 = 100x̄₁ = 109.5 mmσ₁ = 3 mmn₂ = 40x̄₂ = 108.6 mmσ₂ = 8 mm
z =
5.Hard
A sample of 81 measurements has mean 101.1. The population standard deviation is 4. Find the upper limit U of the 95% confidence interval for the mean.
x̄ = 101.1σ = 4n = 8195%
U =
6.Hard
How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 2? The standard deviation is 20. Find the smallest sample size n.
σ = 20E = 299%
n =
Answer key
- 1. p = 0.06944
- 2. z = −1.8
- 3. z = 1.708
- 4. z = 0.6923
- 5. U = 102
- 6. n = 664
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