1.Easy
A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 12 mL. A sample of 100 bottles has a mean of 496.9 mL. Find the test statistic z for H₀: μ = 500.
μ₀ = 500 mLx̄ = 496.9 mLσ = 12 mLn = 100
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.85. Find the p-value p.
z = 1.85H₁: μ > μ₀
p =
3.Medium
Two production lines make the same part. Line 1: a sample of 50 parts has mean length 70.5 mm, and the line's known standard deviation is 3 mm. Line 2: a sample of 60 parts has mean 69.9 mm, known standard deviation 7 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 50x̄₁ = 70.5 mmσ₁ = 3 mmn₂ = 60x̄₂ = 69.9 mmσ₂ = 7 mm
z =
4.Medium
6 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 −0.42 and the standard deviation of the differences is 1.3. Find the paired test statistic t for H₀: μd = 0.
n = 6d̄ = −0.42sd = 1.3
t =
5.Hard
A sample of 64 measurements has mean 117.3. The population standard deviation is 12. Find the lower limit L of the 95% confidence interval for the mean.
x̄ = 117.3σ = 12n = 6495%
L =
6.Hard
A sample of 36 measurements has mean 77.5. The population standard deviation is 10. Find the lower limit L of the 95% confidence interval for the mean.
x̄ = 77.5σ = 10n = 3695%
L =
Answer key
- 1. z = −2.583
- 2. p = 0.03216
- 3. z = 0.601
- 4. t = −0.7914
- 5. L = 114.4
- 6. L = 74.23
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