1.Easy
A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 8 mL. A sample of 16 bottles has a mean of 97.2 mL. Find the test statistic z for H₀: μ = 100.
μ₀ = 100 mLx̄ = 97.2 mLσ = 8 mLn = 16
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 10 mL. A sample of 16 bottles has a mean of 504.3 mL. Find the test statistic z for H₀: μ = 500.
μ₀ = 500 mLx̄ = 504.3 mLσ = 10 mLn = 16
z =
3.Medium
The mean of a population is claimed to be 250; the population standard deviation is known to be 5. A random sample of 100 observations has a mean of 249.39. Test H₀: μ = 250 against H₁: μ < 250. Find the p-value p.
μ₀ = 250σ = 5n = 100x̄ = 249.39H₁: μ < μ₀
p =
4.Medium
A sample of 49 students has a mean score of 50.8 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 50.
μ₀ = 50x̄ = 50.8s = 8n = 49
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 3? The standard deviation is 15. Find the smallest sample size n.
σ = 15E = 395%
n =
6.Hard
A one-sided z test of H₀: μ = 500 against H₁: μ < 500 is done at α = 0.01 with a sample of 100; the standard deviation is known to be 30. In reality the mean is 494.6. Find the power 1 − β of the test in percent.
μ₀ = 500μ = 494.6σ = 30n = 100α = 0.01
1 − β = %
Answer key
- 1. z = −1.4
- 2. z = 1.72
- 3. p = 0.1112
- 4. t = 0.7
- 5. n = 97
- 6. 1 − β = 29.94 %
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