1.Easy
A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 5 mL. A sample of 16 bottles has a mean of 496.8 mL. Find the test statistic z for H₀: μ = 500.
μ₀ = 500 mLx̄ = 496.8 mLσ = 5 mLn = 16
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 8 mL. A sample of 64 bottles has a mean of 121.2 mL. Find the test statistic z for H₀: μ = 120.
μ₀ = 120 mLx̄ = 121.2 mLσ = 8 mLn = 64
z =
3.Medium
A sample of 64 students has a mean score of 501.8 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 500.
μ₀ = 500x̄ = 501.8s = 5n = 64
t =
4.Medium
Two production lines make the same part. Line 1: a sample of 100 parts has mean length 56.5 mm, and the line's known standard deviation is 11 mm. Line 2: a sample of 50 parts has mean 58.8 mm, known standard deviation 19 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 100x̄₁ = 56.5 mmσ₁ = 11 mmn₂ = 50x̄₂ = 58.8 mmσ₂ = 19 mm
z =
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 18. In reality the mean is 39.8. Find the probability of a Type II error β in percent.
μ₀ = 50μ = 39.8σ = 18n = 36α = 0.01
β = %
6.Hard
A sample of 49 measurements has mean 73.2. The population standard deviation is 5. Find the upper limit U of the 95% confidence interval for the mean.
x̄ = 73.2σ = 5n = 4995%
U =
Answer key
- 1. z = −2.56
- 2. z = 1.2
- 3. t = 2.88
- 4. z = −0.7922
- 5. β = 14.14 %
- 6. U = 74.6
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