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
−1.9601.96z = ?

A company claims that a proportion of 0.3 of its customers are satisfied. In a random survey of 250 customers, 63 say they are satisfied. Find the test statistic z for H₀: p = 0.3.

p₀ = 0.3n = 250x = 63
z =
2.Easy
−1.9601.96z = ?

A company claims that a proportion of 0.2 of its customers are satisfied. In a random survey of 200 customers, 54 say they are satisfied. Find the test statistic z for H₀: p = 0.2.

p₀ = 0.2n = 200x = 54
z =
3.Medium
1.1p = ?

The mean of a population is claimed to be 100; the population standard deviation is known to be 12. A random sample of 64 observations has a mean of 101.65. Test H₀: μ = 100 against H₁: μ > 100. Find the p-value p.

μ₀ = 100σ = 12n = 64x̄ = 101.65H₁: μ > μ₀
p =
4.Medium
t −1.99801.998

A sample of 64 students has a mean score of 117.3 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 117.3s = 12n = 64
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 3α = 0.05βσ = 15, power 80%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 3 units with a power of 80%. The standard deviation is 15. Find the minimum sample size n.

α = 0.05power = 80%δ = 3σ = 15zα = 1.645zβ = 0.842
n =
6.Hard
σ = 8, n = ?x̄ − Ex̄ + Ex̄E = 399%

How large must a sample be so that the 99% confidence interval for a mean has a margin of error of at most 3? The standard deviation is 8. Find the smallest sample size n.

σ = 8E = 399%
n =

Answer key

  1. 1. z = −1.656
  2. 2. z = 2.475
  3. 3. p = 0.1357
  4. 4. t = −1.8
  5. 5. n = 155
  6. 6. n = 48

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