1.Easy
A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = −1.54. Find the p-value p.
z = −1.54H₁: μ ≠ μ₀
p =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 15 mL. A sample of 81 bottles has a mean of 52 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 52 mLσ = 15 mLn = 81
z =
3.Medium
7 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 1.51 and the standard deviation of the differences is 1.6. Find the paired test statistic t for H₀: μd = 0.
n = 7d̄ = 1.51sd = 1.6
t =
4.Medium
A sample of 49 students has a mean score of 497.6 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 500.
μ₀ = 500x̄ = 497.6s = 12n = 49
t =
5.Hard
A one-sided z test of H₀: μ = 100 against H₁: μ < 100 is done at α = 0.10 with a sample of 100; the standard deviation is known to be 30. In reality the mean is 93.4. Find the power 1 − β of the test in percent.
μ₀ = 100μ = 93.4σ = 30n = 100α = 0.10
1 − β = %
6.Hard
A one-sided z test of H₀: μ = 200 against H₁: μ < 200 is done at α = 0.10 with a sample of 25; the standard deviation is known to be 15. In reality the mean is 191.9. Find the power 1 − β of the test in percent.
μ₀ = 200μ = 191.9σ = 15n = 25α = 0.10
1 − β = %
Answer key
- 1. p = 0.1236
- 2. z = 1.2
- 3. t = 2.497
- 4. t = −1.4
- 5. 1 − β = 82.07 %
- 6. 1 − β = 92.19 %
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