1.Easy
A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 20 mL. A sample of 100 bottles has a mean of 121.4 mL. Find the test statistic z for H₀: μ = 120.
μ₀ = 120 mLx̄ = 121.4 mLσ = 20 mLn = 100
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 8 mL. A sample of 16 bottles has a mean of 198.2 mL. Find the test statistic z for H₀: μ = 200.
μ₀ = 200 mLx̄ = 198.2 mLσ = 8 mLn = 16
z =
3.Medium
The mean of a population is claimed to be 50; the population standard deviation is known to be 6. A random sample of 144 observations has a mean of 50.93. Test H₀: μ = 50 against H₁: μ > 50. Find the p-value p.
μ₀ = 50σ = 6n = 144x̄ = 50.93H₁: μ > μ₀
p =
4.Medium
Two production lines make the same part. Line 1: a sample of 60 parts has mean length 93 mm, and the line's known standard deviation is 11 mm. Line 2: a sample of 60 parts has mean 89 mm, known standard deviation 13 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 60x̄₁ = 93 mmσ₁ = 11 mmn₂ = 60x̄₂ = 89 mmσ₂ = 13 mm
z =
5.Hard
A one-sided z test at α = 0.05 must detect a shift of the mean of 2 units with a power of 95%. The standard deviation is 10. Find the minimum sample size n.
α = 0.05power = 95%δ = 2σ = 10zα = 1.645zβ = 1.645
n =
6.Hard
A sample of 64 measurements has mean 102.1. The population standard deviation is 12. Find the lower limit L of the 99% confidence interval for the mean.
x̄ = 102.1σ = 12n = 6499%
L =
Answer key
- 1. z = 0.7
- 2. z = −0.9
- 3. p = 0.03144
- 4. z = 1.819
- 5. n = 271
- 6. L = 98.24
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