1.Easy
A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 8 mL. A sample of 100 bottles has a mean of 48.56 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 48.56 mLσ = 8 mLn = 100
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = −1.75. Find the p-value p.
z = −1.75H₁: μ ≠ μ₀
p =
3.Medium
Two teaching methods are compared. Group 1: 6 students, mean score 68, standard deviation 6. Group 2: 6 students, mean score 71.1, standard deviation 11. 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 = 6x̄₁ = 68s₁ = 6n₂ = 6x̄₂ = 71.1s₂ = 11
t =
4.Medium
A sample of 64 students has a mean score of 98.31 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 100.
μ₀ = 100x̄ = 98.31s = 15n = 64
t =
5.Hard
In a trial, 45 of 300 patients on treatment A recover, and 14 of 150 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 45n₁ = 300x₂ = 14n₂ = 150
z =
6.Hard
How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 3? The standard deviation is 5. Find the smallest sample size n.
σ = 5E = 390%
n =
Answer key
- 1. z = −1.8
- 2. p = 0.08012
- 3. t = −0.606
- 4. t = −0.9013
- 5. z = 1.679
- 6. n = 8
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