1.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 36 bottles has a mean of 117.6 mL. Find the test statistic z for H₀: μ = 120.
μ₀ = 120 mLx̄ = 117.6 mLσ = 8 mLn = 36
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A company claims that a proportion of 0.8 of its customers are satisfied. In a random survey of 400 customers, 329 say they are satisfied. Find the test statistic z for H₀: p = 0.8.
p₀ = 0.8n = 400x = 329
z =
3.Medium
Two production lines make the same part. Line 1: a sample of 60 parts has mean length 108.5 mm, and the line's known standard deviation is 16 mm. Line 2: a sample of 60 parts has mean 113.7 mm, known standard deviation 5 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 60x̄₁ = 108.5 mmσ₁ = 16 mmn₂ = 60x̄₂ = 113.7 mmσ₂ = 5 mm
z =
4.Medium
10 employees take a typing test before and after a training course. For each person the difference d = after − before (words per minute) is recorded. The mean difference is −6.26 and the standard deviation of the differences is 5.5. Find the paired test statistic t for H₀: μd = 0.
n = 10d̄ = −6.26sd = 5.5
t =
5.Hard
A sample of 81 measurements has mean 48.7. The population standard deviation is 4. Find the lower limit L of the 99% confidence interval for the mean.
x̄ = 48.7σ = 4n = 8199%
L =
6.Hard
A one-sided z test of H₀: μ = 200 against H₁: μ > 200 is done at α = 0.05 with a sample of 25; the standard deviation is known to be 10. In reality the mean is 203.6. Find the probability of a Type II error β in percent.
μ₀ = 200μ = 203.6σ = 10n = 25α = 0.05
β = %
Answer key
- 1. z = −1.8
- 2. z = 1.125
- 3. z = −2.403
- 4. t = −3.599
- 5. L = 47.56
- 6. β = 43.84 %
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