1.Easy
A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 12 mL. A sample of 100 bottles has a mean of 122.9 mL. Find the test statistic z for H₀: μ = 120.
μ₀ = 120 mLx̄ = 122.9 mLσ = 12 mLn = 100
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is set to fill packs with a mean of 100 g; you suspect it underfills. The standard deviation is known to be 5 g. You will weigh a sample of 100 packs and test H₀: μ = 100 against H₁: μ < 100 at α = 0.01. Below which sample mean x̄c will you reject H₀?
μ₀ = 100 gσ = 5 gn = 100α = 0.01
x̄c = g
3.Medium
A sample of 25 students has a mean score of 202.3 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 200.
μ₀ = 200x̄ = 202.3s = 4n = 25
t =
4.Medium
20 employees take a typing test before and after a training course. For each person the difference d = after − before (words per minute) is recorded. The mean difference is 3.22 and the standard deviation of the differences is 8. Find the paired test statistic t for H₀: μd = 0.
n = 20d̄ = 3.22sd = 8
t =
5.Hard
A one-sided z test of H₀: μ = 50 against H₁: μ > 50 is done at α = 0.05 with a sample of 100; the standard deviation is known to be 15. In reality the mean is 54.35. Find the power 1 − β of the test in percent.
μ₀ = 50μ = 54.35σ = 15n = 100α = 0.05
1 − β = %
6.Hard
In a trial, 54 of 120 patients on treatment A recover, and 57 of 150 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 54n₁ = 120x₂ = 57n₂ = 150
z =
Answer key
- 1. z = 2.417
- 2. x̄c = 98.84 g
- 3. t = 2.875
- 4. t = 1.8
- 5. 1 − β = 89.53 %
- 6. z = 1.162
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