1.Easy
A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 5 mL. A sample of 100 bottles has a mean of 499.6 mL. Find the test statistic z for H₀: μ = 500.
μ₀ = 500 mLx̄ = 499.6 mLσ = 5 mLn = 100
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 5 mL. A sample of 64 bottles has a mean of 118.1 mL. Find the test statistic z for H₀: μ = 120.
μ₀ = 120 mLx̄ = 118.1 mLσ = 5 mLn = 64
z =
3.Medium
A sample of 49 students has a mean score of 500.7 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 500.
μ₀ = 500x̄ = 500.7s = 4n = 49
t =
4.Medium
Two teaching methods are compared. Group 1: 5 students, mean score 68, standard deviation 2. Group 2: 17 students, mean score 52.1, standard deviation 12. 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 = 5x̄₁ = 68s₁ = 2n₂ = 17x̄₂ = 52.1s₂ = 12
t =
5.Hard
In a trial, 83 of 150 patients on treatment A recover, and 155 of 250 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 83n₁ = 150x₂ = 155n₂ = 250
z =
6.Hard
How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 1? The standard deviation is 10. Find the smallest sample size n.
σ = 10E = 199%
n =
Answer key
- 1. z = −0.8
- 2. z = −3.04
- 3. t = 1.225
- 4. t = 2.902
- 5. z = −1.315
- 6. n = 664
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