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 81 bottles has a mean of 101.6 mL. Find the test statistic z for H₀: μ = 100.
μ₀ = 100 mLx̄ = 101.6 mLσ = 20 mLn = 81
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A company claims that a proportion of 0.8 of its customers are satisfied. In a random survey of 120 customers, 86 say they are satisfied. Find the test statistic z for H₀: p = 0.8.
p₀ = 0.8n = 120x = 86
z =
3.Medium
A sample of 36 students has a mean score of 495.5 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 500.
μ₀ = 500x̄ = 495.5s = 15n = 36
t =
4.Medium
Two teaching methods are compared. Group 1: 12 students, mean score 93, standard deviation 11. Group 2: 19 students, mean score 98.8, standard deviation 4. 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 = 12x̄₁ = 93s₁ = 11n₂ = 19x̄₂ = 98.8s₂ = 4
t =
5.Hard
How large must a sample be so that the 99% 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 = 1.599%
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 2.5? The standard deviation is 15. Find the smallest sample size n.
σ = 15E = 2.590%
n =
Answer key
- 1. z = 0.72
- 2. z = −2.282
- 3. t = −1.8
- 4. t = −2.105
- 5. n = 74
- 6. n = 98
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