1.Easy
A company claims that a proportion of 0.75 of its customers are satisfied. In a random survey of 120 customers, 102 say they are satisfied. Find the test statistic z for H₀: p = 0.75.
p₀ = 0.75n = 120x = 102
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 4 mL. A sample of 25 bottles has a mean of 97.92 mL. Find the test statistic z for H₀: μ = 100.
μ₀ = 100 mLx̄ = 97.92 mLσ = 4 mLn = 25
z =
3.Medium
11 employees take a typing test before and after a training course. For each person the difference d = after − before (words per minute) is recorded. The mean difference is 1.6 and the standard deviation of the differences is 1.9. Find the paired test statistic t for H₀: μd = 0.
n = 11d̄ = 1.6sd = 1.9
t =
4.Medium
The mean of a population is claimed to be 100; the population standard deviation is known to be 5. A random sample of 100 observations has a mean of 98.93. Test H₀: μ = 100 against H₁: μ < 100. Find the p-value p.
μ₀ = 100σ = 5n = 100x̄ = 98.93H₁: μ < μ₀
p =
5.Hard
A sample of 36 measurements has mean 509. The population standard deviation is 20. Find the upper limit U of the 95% confidence interval for the mean.
x̄ = 509σ = 20n = 3695%
U =
6.Hard
A one-sided z test of H₀: μ = 80 against H₁: μ > 80 is done at α = 0.10 with a sample of 36; the standard deviation is known to be 18. In reality the mean is 85.1. Find the probability of a Type II error β in percent.
μ₀ = 80μ = 85.1σ = 18n = 36α = 0.10
β = %
Answer key
- 1. z = 2.53
- 2. z = −2.6
- 3. t = 2.793
- 4. p = 0.01618
- 5. U = 515.5
- 6. β = 33.8 %
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