1.Easy
A company claims that a proportion of 0.5 of its customers are satisfied. In a random survey of 250 customers, 141 say they are satisfied. Find the test statistic z for H₀: p = 0.5.
p₀ = 0.5n = 250x = 141
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 10 mL. A sample of 81 bottles has a mean of 78.22 mL. Find the test statistic z for H₀: μ = 75.
μ₀ = 75 mLx̄ = 78.22 mLσ = 10 mLn = 81
z =
3.Medium
A sample of 36 students has a mean score of 97 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 100.
μ₀ = 100x̄ = 97s = 20n = 36
t =
4.Medium
Two production lines make the same part. Line 1: a sample of 60 parts has mean length 110 mm, and the line's known standard deviation is 19 mm. Line 2: a sample of 40 parts has mean 105.8 mm, known standard deviation 16 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 60x̄₁ = 110 mmσ₁ = 19 mmn₂ = 40x̄₂ = 105.8 mmσ₂ = 16 mm
z =
5.Hard
A sample of 25 measurements has mean 194.9. The population standard deviation is 15. Find the upper limit U of the 99% confidence interval for the mean.
x̄ = 194.9σ = 15n = 2599%
U =
6.Hard
How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 2.5? The standard deviation is 20. Find the smallest sample size n.
σ = 20E = 2.595%
n =
Answer key
- 1. z = 2.024
- 2. z = 2.898
- 3. t = −0.9
- 4. z = 1.192
- 5. U = 202.6
- 6. n = 246
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