1.Easy
A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 5 mL. A sample of 81 bottles has a mean of 48.28 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 48.28 mLσ = 5 mLn = 81
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A company claims that a proportion of 0.7 of its customers are satisfied. In a random survey of 200 customers, 124 say they are satisfied. Find the test statistic z for H₀: p = 0.7.
p₀ = 0.7n = 200x = 124
z =
3.Medium
A sample of 100 students has a mean score of 121.2 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 120.
μ₀ = 120x̄ = 121.2s = 5n = 100
t =
4.Medium
A sample of 81 students has a mean score of 52.67 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 50.
μ₀ = 50x̄ = 52.67s = 10n = 81
t =
5.Hard
In a trial, 60 of 150 patients on treatment A recover, and 65 of 120 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 60n₁ = 150x₂ = 65n₂ = 120
z =
6.Hard
A one-sided z test of H₀: μ = 100 against H₁: μ < 100 is done at α = 0.01 with a sample of 100; the standard deviation is known to be 5. In reality the mean is 98.4. Find the power 1 − β of the test in percent.
μ₀ = 100μ = 98.4σ = 5n = 100α = 0.01
1 − β = %
Answer key
- 1. z = −3.096
- 2. z = −2.469
- 3. t = 2.4
- 4. t = 2.403
- 5. z = −2.32
- 6. 1 − β = 80.89 %
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