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 supposed to fill bottles with 500 mL on average. The standard deviation is known to be 8 mL. A sample of 25 bottles has a mean of 503.8 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 503.8 mLσ = 8 mLn = 25

z =

2.Easy

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 12 mL. A sample of 81 bottles has a mean of 51.6 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 51.6 mLσ = 12 mLn = 81

z =

3.Medium

A sample of 64 students has a mean score of 499.4 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 499.4s = 5n = 64

t =

4.Medium

A sample of 100 students has a mean score of 498.6 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 498.6s = 8n = 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 3? The standard deviation is 10. Find the smallest sample size n.

σ = 10E = 399%

n =

6.Hard

A one-sided z test of H₀: μ = 80 against H₁: μ < 80 is done at α = 0.01 with a sample of 64; the standard deviation is known to be 12. In reality the mean is 75.35. Find the probability of a Type II error β in percent.

μ₀ = 80μ = 75.35σ = 12n = 64α = 0.01

β = %

Answer key

1. z = 2.375
2. z = 1.2
3. t = −0.96
4. t = −1.75
5. n = 74
6. β = 21.95 %

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