Hypothesis tests & confidence intervals worksheet with answers

Free printable Hypothesis tests & confidence intervals worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = −1.56. Find the p-value p.

z = −1.56H₁: μ ≠ μ₀

p =

2.Easy

A machine is set to fill packs with a mean of 100 g; you suspect it underfills. The standard deviation is known to be 2 g. You will weigh a sample of 100 packs and test H₀: μ = 100 against H₁: μ < 100 at α = 0.01. Below which sample mean x̄_c will you reject H₀?

μ₀ = 100 gσ = 2 gn = 100α = 0.01

x̄_c = g

3.Medium

The mean of a population is claimed to be 100; the population standard deviation is known to be 30. A random sample of 144 observations has a mean of 96.15. Test H₀: μ = 100 against H₁: μ < 100. Find the p-value p.

μ₀ = 100σ = 30n = 144x̄ = 96.15H₁: μ < μ₀

p =

4.Medium

A sample of 100 students has a mean score of 95.35 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 95.35s = 15n = 100

t =

5.Hard

A one-sided z test of H₀: μ = 200 against H₁: μ < 200 is done at α = 0.05 with a sample of 36; the standard deviation is known to be 12. In reality the mean is 193.8. Find the power 1 − β of the test in percent.

μ₀ = 200μ = 193.8σ = 12n = 36α = 0.05

1 − β = %

6.Hard

A sample of 81 measurements has mean 77.5. The population standard deviation is 15. Find the upper limit U of the 99% confidence interval for the mean.

x̄ = 77.5σ = 15n = 8199%

U =

Answer key

1. p = 0.1188
2. x̄_c = 99.53 g
3. p = 0.06178
4. t = −3.1
5. 1 − β = 92.72 %
6. U = 81.79

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