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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Name: ____________________   Date: ____________

1.Easy
−1.19p = ?

A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −1.19. Find the p-value p.

z = −1.19H₁: μ < μ₀
p =
2.Easy
−1.9601.96z = ?

A company claims that a proportion of 0.75 of its customers are satisfied. In a random survey of 100 customers, 67 say they are satisfied. Find the test statistic z for H₀: p = 0.75.

p₀ = 0.75n = 100x = 67
z =
3.Medium
−2.1792.179t = ?df = 12

13 employees take a typing test before and after a training course. For each person the difference d = after − before (words per minute) is recorded. The mean difference is −4.97 and the standard deviation of the differences is 5.6. Find the paired test statistic t for H₀: μd = 0.

n = 13d̄ = −4.97sd = 5.6
t =
4.Medium
t −1.98401.984

A sample of 100 students has a mean score of 122.5 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 120.

μ₀ = 120x̄ = 122.5s = 15n = 100
t =
5.Hard
z −1.9601.96

A sample of 81 measurements has mean 99.3. The population standard deviation is 4. Find the lower limit L of the 95% confidence interval for the mean.

x̄ = 99.3σ = 4n = 8195%
L =
6.Hard
z −1.9601.96

A sample of 49 measurements has mean 123. The population standard deviation is 10. Find the lower limit L of the 95% confidence interval for the mean.

x̄ = 123σ = 10n = 4995%
L =

Answer key

  1. 1. p = 0.117
  2. 2. z = −1.848
  3. 3. t = −3.2
  4. 4. t = 1.667
  5. 5. L = 98.43
  6. 6. L = 120.2

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