1.Easy
A company claims that a proportion of 0.2 of its customers are satisfied. In a random survey of 400 customers, 94 say they are satisfied. Find the test statistic z for H₀: p = 0.2.
p₀ = 0.2n = 400x = 94
z =
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 100 bottles has a mean of 53.15 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 53.15 mLσ = 15 mLn = 100
z =
3.Medium
A sample of 36 students has a mean score of 495.6 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 500.
μ₀ = 500x̄ = 495.6s = 12n = 36
t =
4.Medium
A sample of 81 students has a mean score of 200.9 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 200.
μ₀ = 200x̄ = 200.9s = 5n = 81
t =
5.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 5. In reality the mean is 198.4. Find the power 1 − β of the test in percent.
μ₀ = 200μ = 198.4σ = 5n = 25α = 0.10
1 − β = %
6.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 506.8. Find the power 1 − β of the test in percent.
μ₀ = 500μ = 506.8σ = 20n = 100α = 0.05
1 − β = %
Answer key
- 1. z = 1.75
- 2. z = 2.1
- 3. t = −2.2
- 4. t = 1.62
- 5. 1 − β = 62.48 %
- 6. 1 − β = 96.04 %
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