1.Easy
A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 15 mL. A sample of 81 bottles has a mean of 504 mL. Find the test statistic z for H₀: μ = 500.
μ₀ = 500 mLx̄ = 504 mLσ = 15 mLn = 81
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 10 mL. A sample of 100 bottles has a mean of 121.7 mL. Find the test statistic z for H₀: μ = 120.
μ₀ = 120 mLx̄ = 121.7 mLσ = 10 mLn = 100
z =
3.Medium
9 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 1.21 and the standard deviation of the differences is 2.8. Find the paired test statistic t for H₀: μd = 0.
n = 9d̄ = 1.21sd = 2.8
t =
4.Medium
Two production lines make the same part. Line 1: a sample of 30 parts has mean length 123 mm, and the line's known standard deviation is 5 mm. Line 2: a sample of 100 parts has mean 120.5 mm, known standard deviation 14 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 30x̄₁ = 123 mmσ₁ = 5 mmn₂ = 100x̄₂ = 120.5 mmσ₂ = 14 mm
z =
5.Hard
In a trial, 83 of 150 patients on treatment A recover, and 100 of 200 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 83n₁ = 150x₂ = 100n₂ = 200
z =
6.Hard
A sample of 81 measurements has mean 48.8. The population standard deviation is 5. Find the lower limit L of the 99% confidence interval for the mean.
x̄ = 48.8σ = 5n = 8199%
L =
Answer key
- 1. z = 2.4
- 2. z = 1.7
- 3. t = 1.296
- 4. z = 1.496
- 5. z = 0.9886
- 6. L = 47.37
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