1.Easy
A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 12 mL. A sample of 36 bottles has a mean of 51.4 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 51.4 mLσ = 12 mLn = 36
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 4 mL. A sample of 16 bottles has a mean of 72.4 mL. Find the test statistic z for H₀: μ = 75.
μ₀ = 75 mLx̄ = 72.4 mLσ = 4 mLn = 16
z =
3.Medium
Two teaching methods are compared. Group 1: 12 students, mean score 88, standard deviation 6.5. Group 2: 19 students, mean score 78.2, standard deviation 8.5. 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 = 12x̄₁ = 88s₁ = 6.5n₂ = 19x̄₂ = 78.2s₂ = 8.5
t =
4.Medium
Two teaching methods are compared. Group 1: 8 students, mean score 67.5, standard deviation 5.5. Group 2: 6 students, mean score 79.5, standard deviation 9.5. 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 = 8x̄₁ = 67.5s₁ = 5.5n₂ = 6x̄₂ = 79.5s₂ = 9.5
t =
5.Hard
A one-sided z test at α = 0.01 must detect a shift of the mean of 2.5 units with a power of 80%. The standard deviation is 18. Find the minimum sample size n.
α = 0.01power = 80%δ = 2.5σ = 18zα = 2.326zβ = 0.842
n =
6.Hard
In a trial, 105 of 150 patients on treatment A recover, and 62 of 100 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 105n₁ = 150x₂ = 62n₂ = 100
z =
Answer key
- 1. z = 0.7
- 2. z = −2.6
- 3. t = 3.407
- 4. t = −2.989
- 5. n = 521
- 6. z = 1.316
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