1.Easy
A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 15 mL. A sample of 36 bottles has a mean of 121.8 mL. Find the test statistic z for H₀: μ = 120.
μ₀ = 120 mLx̄ = 121.8 mLσ = 15 mLn = 36
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 = 1.99. Find the p-value p.
z = 1.99H₁: μ > μ₀
p =
3.Medium
16 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 2.69 and the standard deviation of the differences is 7.7. Find the paired test statistic t for H₀: μd = 0.
n = 16d̄ = 2.69sd = 7.7
t =
4.Medium
A sample of 36 students has a mean score of 121.6 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 120.
μ₀ = 120x̄ = 121.6s = 8n = 36
t =
5.Hard
A one-sided z test of H₀: μ = 80 against H₁: μ > 80 is done at α = 0.01 with a sample of 36; the standard deviation is known to be 12. In reality the mean is 86.4. Find the power 1 − β of the test in percent.
μ₀ = 80μ = 86.4σ = 12n = 36α = 0.01
1 − β = %
6.Hard
A sample of 25 measurements has mean 42.8. The population standard deviation is 20. Find the upper limit U of the 99% confidence interval for the mean.
x̄ = 42.8σ = 20n = 2599%
U =
Answer key
- 1. z = 0.72
- 2. p = 0.0233
- 3. t = 1.397
- 4. t = 1.2
- 5. 1 − β = 80.89 %
- 6. U = 53.1
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