1.Easy
A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 4 mL. A sample of 100 bottles has a mean of 501 mL. Find the test statistic z for H₀: μ = 500.
μ₀ = 500 mLx̄ = 501 mLσ = 4 mLn = 100
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A company claims that a proportion of 0.4 of its customers are satisfied. In a random survey of 120 customers, 34 say they are satisfied. Find the test statistic z for H₀: p = 0.4.
p₀ = 0.4n = 120x = 34
z =
3.Medium
Two production lines make the same part. Line 1: a sample of 60 parts has mean length 71.5 mm, and the line's known standard deviation is 13 mm. Line 2: a sample of 30 parts has mean 66.3 mm, known standard deviation 11 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 60x̄₁ = 71.5 mmσ₁ = 13 mmn₂ = 30x̄₂ = 66.3 mmσ₂ = 11 mm
z =
4.Medium
A sample of 64 students has a mean score of 97.75 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 100.
μ₀ = 100x̄ = 97.75s = 20n = 64
t =
5.Hard
In a trial, 90 of 300 patients on treatment A recover, and 57 of 250 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 90n₁ = 300x₂ = 57n₂ = 250
z =
6.Hard
How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 1.5? The standard deviation is 5. Find the smallest sample size n.
σ = 5E = 1.590%
n =
Answer key
- 1. z = 2.5
- 2. z = −2.609
- 3. z = 1.987
- 4. t = −0.9
- 5. z = 1.9
- 6. n = 31
Full step-by-step solutions: practise this topic on examproblems.com.