1.Easy
A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 15 mL. A sample of 25 bottles has a mean of 82.2 mL. Find the test statistic z for H₀: μ = 75.
μ₀ = 75 mLx̄ = 82.2 mLσ = 15 mLn = 25
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 4 mL. A sample of 16 bottles has a mean of 118.2 mL. Find the test statistic z for H₀: μ = 120.
μ₀ = 120 mLx̄ = 118.2 mLσ = 4 mLn = 16
z =
3.Medium
Two teaching methods are compared. Group 1: 8 students, mean score 92.5, standard deviation 8. Group 2: 18 students, mean score 84, standard deviation 9.5. Assume equal population variances and use the pooled two-sample t test. Find the test statistic t for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (group 1 minus group 2).
n₁ = 8x̄₁ = 92.5s₁ = 8n₂ = 18x̄₂ = 84s₂ = 9.5
t =
4.Medium
Two production lines make the same part. Line 1: a sample of 50 parts has mean length 128.5 mm, and the line's known standard deviation is 9 mm. Line 2: a sample of 60 parts has mean 131 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 = 50x̄₁ = 128.5 mmσ₁ = 9 mmn₂ = 60x̄₂ = 131 mmσ₂ = 19 mm
z =
5.Hard
How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 1? The standard deviation is 12. Find the smallest sample size n.
σ = 12E = 195%
n =
6.Hard
A sample of 16 measurements has mean 198.4. The population standard deviation is 5. Find the lower limit L of the 99% confidence interval for the mean.
x̄ = 198.4σ = 5n = 1699%
L =
Answer key
- 1. z = 2.4
- 2. z = −1.8
- 3. t = 2.201
- 4. z = −0.9047
- 5. n = 554
- 6. L = 195.2
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