1.Easy
A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 20 mL. A sample of 25 bottles has a mean of 209.6 mL. Find the test statistic z for H₀: μ = 200.
μ₀ = 200 mLx̄ = 209.6 mLσ = 20 mLn = 25
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A supplier claims that the mean breaking strength of a cable is 100 kN; you suspect it is higher. The standard deviation is known to be 6 kN. You will take a sample of 16 cables and test H₀: μ = 100 kN against H₁: μ > 100 kN at α = 0.10. Above which sample mean x̄c will you reject H₀?
μ₀ = 100 kNσ = 6 kNn = 16α = 0.10
x̄c = kN
3.Medium
A sample of 81 students has a mean score of 201.9 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 200.
μ₀ = 200x̄ = 201.9s = 10n = 81
t =
4.Medium
Two teaching methods are compared. Group 1: 8 students, mean score 76, standard deviation 10.5. Group 2: 13 students, mean score 64.9, standard deviation 6. 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 = 8x̄₁ = 76s₁ = 10.5n₂ = 13x̄₂ = 64.9s₂ = 6
t =
5.Hard
In a trial, 30 of 150 patients on treatment A recover, and 29 of 100 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 30n₁ = 150x₂ = 29n₂ = 100
z =
6.Hard
A sample of 64 measurements has mean 53.4. The population standard deviation is 15. Find the upper limit U of the 90% confidence interval for the mean.
x̄ = 53.4σ = 15n = 6490%
U =
Answer key
- 1. z = 2.4
- 2. x̄c = 101.9 kN
- 3. t = 1.71
- 4. t = 3.103
- 5. z = −1.642
- 6. U = 56.48
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