1.Easy
A machine is supposed to fill bottles with 200 mL on average. The standard deviation is known to be 20 mL. A sample of 49 bottles has a mean of 193.7 mL. Find the test statistic z for H₀: μ = 200.
μ₀ = 200 mLx̄ = 193.7 mLσ = 20 mLn = 49
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −2.47. Find the p-value p.
z = −2.47H₁: μ < μ₀
p =
3.Medium
A sample of 49 students has a mean score of 202.4 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 200.
μ₀ = 200x̄ = 202.4s = 8n = 49
t =
4.Medium
Two production lines make the same part. Line 1: a sample of 80 parts has mean length 89 mm, and the line's known standard deviation is 13 mm. Line 2: a sample of 30 parts has mean 85.4 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 = 80x̄₁ = 89 mmσ₁ = 13 mmn₂ = 30x̄₂ = 85.4 mmσ₂ = 16 mm
z =
5.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? The standard deviation is 4. Find the smallest sample size n.
σ = 4E = 295%
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 1.5? The standard deviation is 20. Find the smallest sample size n.
σ = 20E = 1.590%
n =
Answer key
- 1. z = −2.205
- 2. p = 0.006756
- 3. t = 2.1
- 4. z = 1.103
- 5. n = 16
- 6. n = 482
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