1.Easy
A company claims that a proportion of 0.25 of its customers are satisfied. In a random survey of 100 customers, 35 say they are satisfied. Find the test statistic z for H₀: p = 0.25.
p₀ = 0.25n = 100x = 35
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A company claims that a proportion of 0.3 of its customers are satisfied. In a random survey of 100 customers, 37 say they are satisfied. Find the test statistic z for H₀: p = 0.3.
p₀ = 0.3n = 100x = 37
z =
3.Medium
Two production lines make the same part. Line 1: a sample of 60 parts has mean length 140 mm, and the line's known standard deviation is 17 mm. Line 2: a sample of 60 parts has mean 133.2 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 = 60x̄₁ = 140 mmσ₁ = 17 mmn₂ = 60x̄₂ = 133.2 mmσ₂ = 8 mm
z =
4.Medium
A sample of 81 students has a mean score of 49.2 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 50.
μ₀ = 50x̄ = 49.2s = 8n = 81
t =
5.Hard
A one-sided z test of H₀: μ = 50 against H₁: μ < 50 is done at α = 0.01 with a sample of 36; the standard deviation is known to be 3. In reality the mean is 49.15. Find the power 1 − β of the test in percent.
μ₀ = 50μ = 49.15σ = 3n = 36α = 0.01
1 − β = %
6.Hard
A sample of 16 measurements has mean 203.8. The population standard deviation is 15. Find the upper limit U of the 95% confidence interval for the mean.
x̄ = 203.8σ = 15n = 1695%
U =
Answer key
- 1. z = 2.309
- 2. z = 1.528
- 3. z = 2.803
- 4. t = −0.9
- 5. 1 − β = 26.57 %
- 6. U = 211.2
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