1.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 64 bottles has a mean of 103.9 mL. Find the test statistic z for H₀: μ = 100.
μ₀ = 100 mLx̄ = 103.9 mLσ = 15 mLn = 64
z =
Hypothesis tests & confidence intervals worksheet with answers
2.Easy
A company claims that a proportion of 0.3 of its customers are satisfied. In a random survey of 150 customers, 36 say they are satisfied. Find the test statistic z for H₀: p = 0.3.
p₀ = 0.3n = 150x = 36
z =
3.Medium
A sample of 64 students has a mean score of 501.2 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 500.
μ₀ = 500x̄ = 501.2s = 4n = 64
t =
4.Medium
The mean of a population is claimed to be 80; the population standard deviation is known to be 16. A random sample of 64 observations has a mean of 77.48. Test H₀: μ = 80 against H₁: μ < 80. Find the p-value p.
μ₀ = 80σ = 16n = 64x̄ = 77.48H₁: μ < μ₀
p =
5.Hard
A one-sided z test of H₀: μ = 100 against H₁: μ > 100 is done at α = 0.10 with a sample of 100; the standard deviation is known to be 15. In reality the mean is 104.5. Find the power 1 − β of the test in percent.
μ₀ = 100μ = 104.5σ = 15n = 100α = 0.10
1 − β = %
6.Hard
In a trial, 56 of 80 patients on treatment A recover, and 85 of 150 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
x₁ = 56n₁ = 80x₂ = 85n₂ = 150
z =
Answer key
- 1. z = 2.08
- 2. z = −1.604
- 3. t = 2.4
- 4. p = 0.1038
- 5. 1 − β = 95.71 %
- 6. z = 1.977
Full step-by-step solutions: practise this topic on examproblems.com.