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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Name: ____________________ Date: ____________

1.Easy

A supplier claims that the mean breaking strength of a cable is 200 kN; you suspect it is higher. The standard deviation is known to be 3 kN. You will take a sample of 64 cables and test H₀: μ = 200 kN against H₁: μ > 200 kN at α = 0.01. Above which sample mean x̄_c will you reject H₀?

μ₀ = 200 kNσ = 3 kNn = 64α = 0.01

x̄_c = kN

2.Easy

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 4 mL. A sample of 64 bottles has a mean of 48.7 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 48.7 mLσ = 4 mLn = 64

z =

3.Medium

A sample of 36 students has a mean score of 76 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 76s = 5n = 36

t =

4.Medium

A sample of 100 students has a mean score of 98.32 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 98.32s = 12n = 100

t =

5.Hard

How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 0.5? The standard deviation is 20. Find the smallest sample size n.

σ = 20E = 0.599%

n =

6.Hard

A sample of 100 measurements has mean 99.4. The population standard deviation is 5. Find the upper limit U of the 95% confidence interval for the mean.

x̄ = 99.4σ = 5n = 10095%

U =

Answer key

1. x̄_c = 200.9 kN
2. z = −2.6
3. t = 1.2
4. t = −1.4
5. n = 10618
6. U = 100.4

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