1.Easy
A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 8 mL. A sample of 49 bottles has a mean of 119 mL. Find the test statistic z for H₀: μ = 120.
μ₀ = 120 mLx̄ = 119 mLσ = 8 mLn = 49
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 15 mL. A sample of 16 bottles has a mean of 104.5 mL. Find the test statistic z for H₀: μ = 100.
μ₀ = 100 mLx̄ = 104.5 mLσ = 15 mLn = 16
z =
3.Medium
The mean of a population is claimed to be 120; the population standard deviation is known to be 4. A random sample of 64 observations has a mean of 120.93. Test H₀: μ = 120 against H₁: μ > 120. Find the p-value p.
μ₀ = 120σ = 4n = 64x̄ = 120.93H₁: μ > μ₀
p =
4.Medium
The mean of a population is claimed to be 250; the population standard deviation is known to be 8. A random sample of 64 observations has a mean of 252.36. Test H₀: μ = 250 against H₁: μ > 250. Find the p-value p.
μ₀ = 250σ = 8n = 64x̄ = 252.36H₁: μ > μ₀
p =
5.Hard
A one-sided z test of H₀: μ = 50 against H₁: μ < 50 is done at α = 0.05 with a sample of 100; the standard deviation is known to be 10. In reality the mean is 49. Find the probability of a Type II error β in percent.
μ₀ = 50μ = 49σ = 10n = 100α = 0.05
β = %
6.Hard
A sample of 81 measurements has mean 51. The population standard deviation is 8. Find the upper limit U of the 99% confidence interval for the mean.
x̄ = 51σ = 8n = 8199%
U =
Answer key
- 1. z = −0.875
- 2. z = 1.2
- 3. p = 0.03144
- 4. p = 0.009137
- 5. β = 74.05 %
- 6. U = 53.29
Full step-by-step solutions: practise this topic on examproblems.com.