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 company claims that a proportion of 0.7 of its customers are satisfied. In a random survey of 100 customers, 79 say they are satisfied. Find the test statistic z for H₀: p = 0.7.

p₀ = 0.7n = 100x = 79

z =

2.Easy

A machine is set to fill packs with a mean of 200 g; you suspect it underfills. The standard deviation is known to be 6 g. You will weigh a sample of 64 packs and test H₀: μ = 200 against H₁: μ < 200 at α = 0.10. Below which sample mean x̄_c will you reject H₀?

μ₀ = 200 gσ = 6 gn = 64α = 0.10

x̄_c = g

3.Medium

A sample of 16 students has a mean score of 496.5 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 496.5s = 10n = 16

t =

4.Medium

A sample of 81 students has a mean score of 101.6 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 101.6s = 5n = 81

t =

5.Hard

A sample of 16 measurements has mean 196.2. The population standard deviation is 8. Find the lower limit L of the 95% confidence interval for the mean.

x̄ = 196.2σ = 8n = 1695%

L =

6.Hard

A one-sided z test of H₀: μ = 200 against H₁: μ < 200 is done at α = 0.05 with a sample of 25; the standard deviation is known to be 10. In reality the mean is 195.4. Find the power 1 − β of the test in percent.

μ₀ = 200μ = 195.4σ = 10n = 25α = 0.05

1 − β = %

Answer key

1. z = 1.964
2. x̄_c = 199 g
3. t = −1.4
4. t = 2.88
5. L = 192.3
6. 1 − β = 74.38 %

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