1.Easy
A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 8 mL. A sample of 81 bottles has a mean of 48.76 mL. Find the test statistic z for H₀: μ = 50.
μ₀ = 50 mLx̄ = 48.76 mLσ = 8 mLn = 81
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A company claims that a proportion of 0.7 of its customers are satisfied. In a random survey of 150 customers, 89 say they are satisfied. Find the test statistic z for H₀: p = 0.7.
p₀ = 0.7n = 150x = 89
z =
3.Medium
A sample of 81 students has a mean score of 199.4 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 200.
μ₀ = 200x̄ = 199.4s = 4n = 81
t =
4.Medium
Two production lines make the same part. Line 1: a sample of 30 parts has mean length 99.5 mm, and the line's known standard deviation is 8 mm. Line 2: a sample of 30 parts has mean 92.3 mm, known standard deviation 10 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).
n₁ = 30x̄₁ = 99.5 mmσ₁ = 8 mmn₂ = 30x̄₂ = 92.3 mmσ₂ = 10 mm
z =
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 5. Find the smallest sample size n.
σ = 5E = 2.590%
n =
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 3? The standard deviation is 10. Find the smallest sample size n.
σ = 10E = 390%
n =
Answer key
- 1. z = −1.395
- 2. z = −2.851
- 3. t = −1.35
- 4. z = 3.079
- 5. n = 11
- 6. n = 31
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