1.Easy
A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 20 mL. A sample of 64 bottles has a mean of 97.75 mL. Find the test statistic z for H₀: μ = 100.
μ₀ = 100 mLx̄ = 97.75 mLσ = 20 mLn = 64
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A company claims that a proportion of 0.5 of its customers are satisfied. In a random survey of 500 customers, 224 say they are satisfied. Find the test statistic z for H₀: p = 0.5.
p₀ = 0.5n = 500x = 224
z =
3.Medium
A sample of 16 students has a mean score of 132 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 120.
μ₀ = 120x̄ = 132s = 20n = 16
t =
4.Medium
Two teaching methods are compared. Group 1: 5 students, mean score 50.5, standard deviation 2. Group 2: 17 students, mean score 56.9, standard deviation 5.5. 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 = 50.5s₁ = 2n₂ = 17x̄₂ = 56.9s₂ = 5.5
t =
5.Hard
How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 2.5? The standard deviation is 8. Find the smallest sample size n.
σ = 8E = 2.590%
n =
6.Hard
In a trial, 75 of 300 patients on treatment A recover, and 60 of 300 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 75n₁ = 300x₂ = 60n₂ = 300
z =
Answer key
- 1. z = −0.9
- 2. z = −2.326
- 3. t = 2.4
- 4. t = −2.516
- 5. n = 28
- 6. z = 1.466
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