1.Easy
A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 5 mL. A sample of 16 bottles has a mean of 46.75 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 46.75 mLσ = 5 mLn = 16
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 5 mL. A sample of 64 bottles has a mean of 51.31 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 51.31 mLσ = 5 mLn = 64
z =
3.Medium
8 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 −1.06 and the standard deviation of the differences is 1.2. Find the paired test statistic t for H₀: μd = 0.
n = 8d̄ = −1.06sd = 1.2
t =
4.Medium
Two teaching methods are compared. Group 1: 10 students, mean score 56.5, standard deviation 7.5. Group 2: 12 students, mean score 53.2, standard deviation 8. 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 = 10x̄₁ = 56.5s₁ = 7.5n₂ = 12x̄₂ = 53.2s₂ = 8
t =
5.Hard
A sample of 81 measurements has mean 121.3. The population standard deviation is 15. Find the upper limit U of the 90% confidence interval for the mean.
x̄ = 121.3σ = 15n = 8190%
U =
6.Hard
In a trial, 16 of 80 patients on treatment A recover, and 11 of 150 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 16n₁ = 80x₂ = 11n₂ = 150
z =
Answer key
- 1. z = −2.6
- 2. z = 2.096
- 3. t = −2.498
- 4. t = 0.9908
- 5. U = 124
- 6. z = 2.842
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