1.Easy
A company claims that a proportion of 0.2 of its customers are satisfied. In a random survey of 100 customers, 30 say they are satisfied. Find the test statistic z for H₀: p = 0.2.
p₀ = 0.2n = 100x = 30
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 = 1.18. Find the p-value p.
z = 1.18H₁: μ ≠ μ₀
p =
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 −0.87 and the standard deviation of the differences is 1. Find the paired test statistic t for H₀: μd = 0.
n = 9d̄ = −0.87sd = 1
t =
4.Medium
12 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 −3.18 and the standard deviation of the differences is 2.9. Find the paired test statistic t for H₀: μd = 0.
n = 12d̄ = −3.18sd = 2.9
t =
5.Hard
A one-sided z test of H₀: μ = 500 against H₁: μ < 500 is done at α = 0.05 with a sample of 100; the standard deviation is known to be 20. In reality the mean is 493.4. Find the power 1 − β of the test in percent.
μ₀ = 500μ = 493.4σ = 20n = 100α = 0.05
1 − β = %
6.Hard
A sample of 36 measurements has mean 46.3. The population standard deviation is 8. Find the upper limit U of the 95% confidence interval for the mean.
x̄ = 46.3σ = 8n = 3695%
U =
Answer key
- 1. z = 2.5
- 2. p = 0.238
- 3. t = −2.61
- 4. t = −3.799
- 5. 1 − β = 95.1 %
- 6. U = 48.91
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