1.Easy
A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.08. Find the p-value p.
z = 1.08H₁: μ > μ₀
p =
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 15 mL. A sample of 49 bottles has a mean of 203.6 mL. Find the test statistic z for H₀: μ = 200.
μ₀ = 200 mLx̄ = 203.6 mLσ = 15 mLn = 49
z =
3.Medium
The mean of a population is claimed to be 500; the population standard deviation is known to be 6. A random sample of 36 observations has a mean of 497.82. Test H₀: μ = 500 against H₁: μ ≠ 500. Find the p-value p.
μ₀ = 500σ = 6n = 36x̄ = 497.82H₁: μ ≠ μ₀
p =
4.Medium
Two teaching methods are compared. Group 1: 9 students, mean score 30, standard deviation 7. Group 2: 5 students, mean score 32.8, standard deviation 10.5. 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 = 9x̄₁ = 30s₁ = 7n₂ = 5x̄₂ = 32.8s₂ = 10.5
t =
5.Hard
In a trial, 120 of 300 patients on treatment A recover, and 66 of 150 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 120n₁ = 300x₂ = 66n₂ = 150
z =
6.Hard
In a trial, 120 of 200 patients on treatment A recover, and 111 of 150 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 120n₁ = 200x₂ = 111n₂ = 150
z =
Answer key
- 1. p = 0.1401
- 2. z = 1.68
- 3. p = 0.02926
- 4. t = −0.6025
- 5. z = −0.8123
- 6. z = −2.736
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