1.Easy
A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 12 mL. A sample of 81 bottles has a mean of 198.1 mL. Find the test statistic z for H₀: μ = 200.
μ₀ = 200 mLx̄ = 198.1 mLσ = 12 mLn = 81
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A company claims that a proportion of 0.3 of its customers are satisfied. In a random survey of 250 customers, 66 say they are satisfied. Find the test statistic z for H₀: p = 0.3.
p₀ = 0.3n = 250x = 66
z =
3.Medium
A sample of 25 students has a mean score of 77.1 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 75.
μ₀ = 75x̄ = 77.1s = 5n = 25
t =
4.Medium
Two teaching methods are compared. Group 1: 25 students, mean score 104.5, standard deviation 8.5. Group 2: 6 students, mean score 111.1, standard deviation 5. Assume equal population variances and use the pooled two-sample t test. Find the test statistic t for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (group 1 minus group 2).
n₁ = 25x̄₁ = 104.5s₁ = 8.5n₂ = 6x̄₂ = 111.1s₂ = 5
t =
5.Hard
A one-sided z test of H₀: μ = 50 against H₁: μ > 50 is done at α = 0.01 with a sample of 64; the standard deviation is known to be 4. In reality the mean is 51.1. Find the power 1 − β of the test in percent.
μ₀ = 50μ = 51.1σ = 4n = 64α = 0.01
1 − β = %
6.Hard
A one-sided z test of H₀: μ = 500 against H₁: μ > 500 is done at α = 0.01 with a sample of 64; the standard deviation is known to be 20. In reality the mean is 507.5. Find the power 1 − β of the test in percent.
μ₀ = 500μ = 507.5σ = 20n = 64α = 0.01
1 − β = %
Answer key
- 1. z = −1.425
- 2. z = −1.242
- 3. t = 2.1
- 4. t = −1.813
- 5. 1 − β = 44.99 %
- 6. 1 − β = 74.98 %
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