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 100 mL on average. The standard deviation is known to be 20 mL. A sample of 81 bottles has a mean of 98 mL. Find the test statistic z for H₀: μ = 100.

μ₀ = 100 mLx̄ = 98 mLσ = 20 mLn = 81

z =

2.Easy

A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 10 mL. A sample of 25 bottles has a mean of 117.2 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 117.2 mLσ = 10 mLn = 25

z =

3.Medium

A sample of 25 students has a mean score of 76.12 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 76.12s = 8n = 25

t =

4.Medium

The mean of a population is claimed to be 100; the population standard deviation is known to be 3. A random sample of 36 observations has a mean of 98.91. Test H₀: μ = 100 against H₁: μ < 100. Find the p-value p.

μ₀ = 100σ = 3n = 36x̄ = 98.91H₁: μ < μ₀

p =

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 10. Find the smallest sample size n.

σ = 10E = 290%

n =

6.Hard

How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 3? The standard deviation is 20. Find the smallest sample size n.

σ = 20E = 390%

n =

Answer key

1. z = −0.9
2. z = −1.4
3. t = 0.7
4. p = 0.01463
5. n = 68
6. n = 121

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