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 20 mL. A sample of 25 bottles has a mean of 487.6 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 487.6 mLσ = 20 mLn = 25

z =

2.Easy

A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 20 mL. A sample of 25 bottles has a mean of 94.4 mL. Find the test statistic z for H₀: μ = 100.

μ₀ = 100 mLx̄ = 94.4 mLσ = 20 mLn = 25

z =

3.Medium

A sample of 64 students has a mean score of 504.5 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 504.5s = 15n = 64

t =

4.Medium

9 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 9.58 and the standard deviation of the differences is 11.5. Find the paired test statistic t for H₀: μ_d = 0.

n = 9d̄ = 9.58s_d = 11.5

t =

5.Hard

A sample of 36 measurements has mean 54.7. The population standard deviation is 10. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 54.7σ = 10n = 3699%

L =

6.Hard

A sample of 25 measurements has mean 202. The population standard deviation is 4. Find the upper limit U of the 95% confidence interval for the mean.

x̄ = 202σ = 4n = 2595%

U =

Answer key

1. z = −3.1
2. z = −1.4
3. t = 2.4
4. t = 2.499
5. L = 50.41
6. U = 203.6

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