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 z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 1.97. Find the p-value p.

z = 1.97H₁: μ > μ₀

p =

2.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 49 bottles has a mean of 106 mL. Find the test statistic z for H₀: μ = 100.

μ₀ = 100 mLx̄ = 106 mLσ = 20 mLn = 49

z =

3.Medium

The mean of a population is claimed to be 120; the population standard deviation is known to be 24. A random sample of 64 observations has a mean of 125.88. Test H₀: μ = 120 against H₁: μ > 120. Find the p-value p.

μ₀ = 120σ = 24n = 64x̄ = 125.88H₁: μ > μ₀

p =

4.Medium

The mean of a population is claimed to be 50; the population standard deviation is known to be 30. A random sample of 100 observations has a mean of 45.32. Test H₀: μ = 50 against H₁: μ ≠ 50. Find the p-value p.

μ₀ = 50σ = 30n = 100x̄ = 45.32H₁: 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 0.5? The standard deviation is 15. Find the smallest sample size n.

σ = 15E = 0.590%

n =

6.Hard

A one-sided z test of H₀: μ = 500 against H₁: μ < 500 is done at α = 0.05 with a sample of 64; the standard deviation is known to be 4. In reality the mean is 499.35. Find the probability of a Type II error β in percent.

μ₀ = 500μ = 499.35σ = 4n = 64α = 0.05

β = %

Answer key

1. p = 0.02442
2. z = 2.1
3. p = 0.025
4. p = 0.1188
5. n = 2436
6. β = 63.5 %

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