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 5 mL. A sample of 25 bottles has a mean of 502.4 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 502.4 mLσ = 5 mLn = 25

z =

2.Easy

A machine is set to fill packs with a mean of 50 g; you suspect it underfills. The standard deviation is known to be 10 g. You will weigh a sample of 64 packs and test H₀: μ = 50 against H₁: μ < 50 at α = 0.05. Below which sample mean x̄_c will you reject H₀?

μ₀ = 50 gσ = 10 gn = 64α = 0.05

x̄_c = g

3.Medium

A sample of 16 students has a mean score of 53.63 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 53.63s = 5n = 16

t =

4.Medium

A sample of 81 students has a mean score of 117.6 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 117.6s = 10n = 81

t =

5.Hard

How large must a sample be so that the 95% 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 = 295%

n =

6.Hard

In a trial, 83 of 150 patients on treatment A recover, and 50 of 120 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 83n₁ = 150x₂ = 50n₂ = 120

z =

Answer key

1. z = 2.4
2. x̄_c = 47.94 g
3. t = 2.904
4. t = −2.16
5. n = 97
6. z = 2.232

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