1.Easy
A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 12 mL. A sample of 100 bottles has a mean of 201.4 mL. Find the test statistic z for H₀: μ = 200.
μ₀ = 200 mLx̄ = 201.4 mLσ = 12 mLn = 100
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 4 mL. A sample of 49 bottles has a mean of 100.7 mL. Find the test statistic z for H₀: μ = 100.
μ₀ = 100 mLx̄ = 100.7 mLσ = 4 mLn = 49
z =
3.Medium
The mean of a population is claimed to be 120; the population standard deviation is known to be 4. A random sample of 64 observations has a mean of 120.74. Test H₀: μ = 120 against H₁: μ > 120. Find the p-value p.
μ₀ = 120σ = 4n = 64x̄ = 120.74H₁: μ > μ₀
p =
4.Medium
Two production lines make the same part. Line 1: a sample of 60 parts has mean length 84 mm, and the line's known standard deviation is 17 mm. Line 2: a sample of 100 parts has mean 81 mm, known standard deviation 16 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 60x̄₁ = 84 mmσ₁ = 17 mmn₂ = 100x̄₂ = 81 mmσ₂ = 16 mm
z =
5.Hard
A sample of 49 measurements has mean 503.4. The population standard deviation is 20. Find the lower limit L of the 90% confidence interval for the mean.
x̄ = 503.4σ = 20n = 4990%
L =
6.Hard
A one-sided z test at α = 0.05 must detect a shift of the mean of 5 units with a power of 95%. The standard deviation is 19. Find the minimum sample size n.
α = 0.05power = 95%δ = 5σ = 19zα = 1.645zβ = 1.645
n =
Answer key
- 1. z = 1.167
- 2. z = 1.225
- 3. p = 0.06944
- 4. z = 1.105
- 5. L = 498.7
- 6. n = 157
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