1.Easy
A company claims that a proportion of 0.2 of its customers are satisfied. In a random survey of 100 customers, 10 say they are satisfied. Find the test statistic z for H₀: p = 0.2.
p₀ = 0.2n = 100x = 10
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −2.04. Find the p-value p.
z = −2.04H₁: μ < μ₀
p =
3.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 9 mm. Line 2: a sample of 50 parts has mean 114.4 mm, known standard deviation 11 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 = 9 mmn₂ = 50x̄₂ = 114.4 mmσ₂ = 11 mm
z =
4.Medium
A sample of 100 students has a mean score of 48.9 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 50.
μ₀ = 50x̄ = 48.9s = 5n = 100
t =
5.Hard
How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 1? The standard deviation is 12. Find the smallest sample size n.
σ = 12E = 199%
n =
6.Hard
A one-sided z test of H₀: μ = 500 against H₁: μ < 500 is done at α = 0.05 with a sample of 100; the standard deviation is known to be 10. In reality the mean is 497.8. Find the power 1 − β of the test in percent.
μ₀ = 500μ = 497.8σ = 10n = 100α = 0.05
1 − β = %
Answer key
- 1. z = −2.5
- 2. p = 0.02068
- 3. z = −2.726
- 4. t = −2.2
- 5. n = 956
- 6. 1 − β = 71.06 %
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