1.Easy
A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 8 mL. A sample of 36 bottles has a mean of 70.87 mL. Find the test statistic z for H₀: μ = 75.
μ₀ = 75 mLx̄ = 70.87 mLσ = 8 mLn = 36
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 250 customers, 163 say they are satisfied. Find the test statistic z for H₀: p = 0.7.
p₀ = 0.7n = 250x = 163
z =
3.Medium
A sample of 36 students has a mean score of 76.13 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 75.
μ₀ = 75x̄ = 76.13s = 4n = 36
t =
4.Medium
Two teaching methods are compared. Group 1: 8 students, mean score 79.5, standard deviation 5. Group 2: 8 students, mean score 81.9, standard deviation 7. 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 = 8x̄₁ = 79.5s₁ = 5n₂ = 8x̄₂ = 81.9s₂ = 7
t =
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 8. Find the smallest sample size n.
σ = 8E = 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? The standard deviation is 12. Find the smallest sample size n.
σ = 12E = 190%
n =
Answer key
- 1. z = −3.097
- 2. z = −1.656
- 3. t = 1.695
- 4. t = −0.7891
- 5. n = 62
- 6. n = 390
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