1.Easy
A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 12 mL. A sample of 64 bottles has a mean of 47.9 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 47.9 mLσ = 12 mLn = 64
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A company claims that a proportion of 0.25 of its customers are satisfied. In a random survey of 150 customers, 22 say they are satisfied. Find the test statistic z for H₀: p = 0.25.
p₀ = 0.25n = 150x = 22
z =
3.Medium
A sample of 81 students has a mean score of 199.2 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 200.
μ₀ = 200x̄ = 199.2s = 5n = 81
t =
4.Medium
Two production lines make the same part. Line 1: a sample of 80 parts has mean length 113 mm, and the line's known standard deviation is 4 mm. Line 2: a sample of 30 parts has mean 113.8 mm, known standard deviation 3 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 80x̄₁ = 113 mmσ₁ = 4 mmn₂ = 30x̄₂ = 113.8 mmσ₂ = 3 mm
z =
5.Hard
A sample of 25 measurements has mean 198.3. The population standard deviation is 4. Find the upper limit U of the 99% confidence interval for the mean.
x̄ = 198.3σ = 4n = 2599%
U =
6.Hard
A one-sided z test at α = 0.01 must detect a shift of the mean of 2 units with a power of 95%. The standard deviation is 8. Find the minimum sample size n.
α = 0.01power = 95%δ = 2σ = 8zα = 2.326zβ = 1.645
n =
Answer key
- 1. z = −1.4
- 2. z = −2.923
- 3. t = −1.44
- 4. z = −1.131
- 5. U = 200.4
- 6. n = 253
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