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 machine is set to fill packs with a mean of 100 g; you suspect it underfills. The standard deviation is known to be 10 g. You will weigh a sample of 36 packs and test H₀: μ = 100 against H₁: μ < 100 at α = 0.10. Below which sample mean x̄_c will you reject H₀?

μ₀ = 100 gσ = 10 gn = 36α = 0.10

x̄_c = g

2.Easy

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 8 mL. A sample of 64 bottles has a mean of 52.1 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 52.1 mLσ = 8 mLn = 64

z =

3.Medium

A sample of 36 students has a mean score of 101.8 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 101.8s = 5n = 36

t =

4.Medium

A sample of 49 students has a mean score of 46.23 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 46.23s = 12n = 49

t =

5.Hard

How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 2? The standard deviation is 8. Find the smallest sample size n.

σ = 8E = 290%

n =

6.Hard

A sample of 16 measurements has mean 75.6. The population standard deviation is 12. Find the upper limit U of the 95% confidence interval for the mean.

x̄ = 75.6σ = 12n = 1695%

U =

Answer key

1. x̄_c = 97.86 g
2. z = 2.1
3. t = 2.16
4. t = −2.199
5. n = 44
6. U = 81.48

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