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 0.5 of its customers are satisfied. In a random survey of 500 customers, 235 say they are satisfied. Find the test statistic z for H₀: p = 0.5.

p₀ = 0.5n = 500x = 235
z =
2.Easy
z −1.9601.96

A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 10 mL. A sample of 16 bottles has a mean of 112.3 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 112.3 mLσ = 10 mLn = 16
z =
3.Medium
−2.38p = ?

The mean of a population is claimed to be 80; the population standard deviation is known to be 15. A random sample of 100 observations has a mean of 76.43. Test H₀: μ = 80 against H₁: μ < 80. Find the p-value p.

μ₀ = 80σ = 15n = 100x̄ = 76.43H₁: μ < μ₀
p =
4.Medium
t −1.9901.99

A sample of 81 students has a mean score of 98.62 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 98.62s = 4n = 81
t =
5.Hard
z −2.57602.576

A sample of 100 measurements has mean 74.4. The population standard deviation is 10. Find the upper limit U of the 99% confidence interval for the mean.

x̄ = 74.4σ = 10n = 10099%
U =
6.Hard
z −1.9601.96

A sample of 25 measurements has mean 97. The population standard deviation is 5. Find the lower limit L of the 95% confidence interval for the mean.

x̄ = 97σ = 5n = 2595%
L =

Answer key

  1. 1. z = −1.342
  2. 2. z = −3.08
  3. 3. p = 0.008656
  4. 4. t = −3.105
  5. 5. U = 76.98
  6. 6. L = 95.04

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