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
−1.9601.96z = ?

A company claims that a proportion of 0.75 of its customers are satisfied. In a random survey of 100 customers, 84 say they are satisfied. Find the test statistic z for H₀: p = 0.75.

p₀ = 0.75n = 100x = 84
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 12 mL. A sample of 100 bottles has a mean of 497.4 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 497.4 mLσ = 12 mLn = 100
z =
3.Medium
t −1.98401.984

A sample of 100 students has a mean score of 50.84 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 50.84s = 4n = 100
t =
4.Medium
t −2.13102.131

A sample of 16 students has a mean score of 62 and a sample standard deviation of 20. Find the test statistic t for H₀: μ = 50.

μ₀ = 50x̄ = 62s = 20n = 16
t =
5.Hard
z −2.57602.576

A sample of 25 measurements has mean 74.4. The population standard deviation is 4. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 74.4σ = 4n = 2599%
L =
6.Hard
σ = 4, n = ?x̄ − Ex̄ + Ex̄E = 1.595%

How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 1.5? The standard deviation is 4. Find the smallest sample size n.

σ = 4E = 1.595%
n =

Answer key

  1. 1. z = 2.078
  2. 2. z = −2.167
  3. 3. t = 2.1
  4. 4. t = 2.4
  5. 5. L = 72.34
  6. 6. n = 28

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