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 15 mL. A sample of 25 bottles has a mean of 490.7 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 490.7 mLσ = 15 mLn = 25

z =

2.Easy

A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 5 mL. A sample of 16 bottles has a mean of 97.75 mL. Find the test statistic z for H₀: μ = 100.

μ₀ = 100 mLx̄ = 97.75 mLσ = 5 mLn = 16

z =

3.Medium

The mean of a population is claimed to be 500; the population standard deviation is known to be 30. A random sample of 144 observations has a mean of 506. Test H₀: μ = 500 against H₁: μ > 500. Find the p-value p.

μ₀ = 500σ = 30n = 144x̄ = 506H₁: μ > μ₀

p =

4.Medium

A sample of 16 students has a mean score of 43.8 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 43.8s = 8n = 16

t =

5.Hard

A sample of 81 measurements has mean 102. The population standard deviation is 15. Find the lower limit L of the 90% confidence interval for the mean.

x̄ = 102σ = 15n = 8190%

L =

6.Hard

A one-sided z test at α = 0.01 must detect a shift of the mean of 5 units with a power of 80%. The standard deviation is 12. Find the minimum sample size n.

α = 0.01power = 80%δ = 5σ = 12z_α = 2.326z_β = 0.842

n =

Answer key

1. z = −3.1
2. z = −1.8
3. p = 0.008198
4. t = −3.1
5. L = 99.26
6. n = 58

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