1.Easy
A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 10 mL. A sample of 49 bottles has a mean of 46.29 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 46.29 mLσ = 10 mLn = 49
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 4 mL. A sample of 64 bottles has a mean of 200.8 mL. Find the test statistic z for H₀: μ = 200.
μ₀ = 200 mLx̄ = 200.8 mLσ = 4 mLn = 64
z =
3.Medium
A sample of 100 students has a mean score of 197.4 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 200.
μ₀ = 200x̄ = 197.4s = 10n = 100
t =
4.Medium
Two teaching methods are compared. Group 1: 9 students, mean score 117, standard deviation 9. Group 2: 8 students, mean score 113.4, standard deviation 2. 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 = 9x̄₁ = 117s₁ = 9n₂ = 8x̄₂ = 113.4s₂ = 2
t =
5.Hard
In a trial, 120 of 200 patients on treatment A recover, and 201 of 300 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 120n₁ = 200x₂ = 201n₂ = 300
z =
6.Hard
In a trial, 56 of 80 patients on treatment A recover, and 67 of 80 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 56n₁ = 80x₂ = 67n₂ = 80
z =
Answer key
- 1. z = −2.597
- 2. z = 1.6
- 3. t = −2.6
- 4. t = 1.104
- 5. z = −1.599
- 6. z = −2.063
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