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 0.25 of its customers are satisfied. In a random survey of 100 customers, 37 say they are satisfied. Find the test statistic z for H₀: p = 0.25.

p₀ = 0.25n = 100x = 37

z =

2.Easy

A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.68. Find the p-value p.

z = 1.68H₁: μ > μ₀

p =

3.Medium

The mean of a population is claimed to be 100; the population standard deviation is known to be 24. A random sample of 144 observations has a mean of 96.8. Test H₀: μ = 100 against H₁: μ < 100. Find the p-value p.

μ₀ = 100σ = 24n = 144x̄ = 96.8H₁: μ < μ₀

p =

4.Medium

The mean of a population is claimed to be 80; the population standard deviation is known to be 40. A random sample of 100 observations has a mean of 86.88. Test H₀: μ = 80 against H₁: μ > 80. Find the p-value p.

μ₀ = 80σ = 40n = 100x̄ = 86.88H₁: μ > μ₀

p =

5.Hard

A sample of 16 measurements has mean 88. The population standard deviation is 20. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 88σ = 20n = 1699%

L =

6.Hard

A one-sided z test at α = 0.05 must detect a shift of the mean of 1 units with a power of 80%. The standard deviation is 10. Find the minimum sample size n.

α = 0.05power = 80%δ = 1σ = 10z_α = 1.645z_β = 0.842

n =

Answer key

1. z = 2.771
2. p = 0.04648
3. p = 0.0548
4. p = 0.04272
5. L = 75.12
6. n = 619

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