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 120 customers, 46 say they are satisfied. Find the test statistic z for H₀: p = 0.3.

p₀ = 0.3n = 120x = 46
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 4 mL. A sample of 16 bottles has a mean of 496.9 mL. Find the test statistic z for H₀: μ = 500.

μ₀ = 500 mLx̄ = 496.9 mLσ = 4 mLn = 16
z =
3.Medium
t −2.0302.03

A sample of 36 students has a mean score of 98.5 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 98.5s = 5n = 36
t =
4.Medium
t −2.13102.131

A sample of 16 students has a mean score of 82.2 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 82.2s = 12n = 16
t =
5.Hard
μ₀x̄c

A one-sided z test of H₀: μ = 80 against H₁: μ < 80 is done at α = 0.01 with a sample of 36; the standard deviation is known to be 15. In reality the mean is 70.5. Find the power 1 − β of the test in percent.

μ₀ = 80μ = 70.5σ = 15n = 36α = 0.01
1 − β = %
6.Hard
z −1.9601.96

A sample of 100 measurements has mean 50.6. The population standard deviation is 5. Find the lower limit L of the 95% confidence interval for the mean.

x̄ = 50.6σ = 5n = 10095%
L =

Answer key

  1. 1. z = 1.992
  2. 2. z = −3.1
  3. 3. t = −1.8
  4. 4. t = 2.4
  5. 5. 1 − β = 92.98 %
  6. 6. L = 49.62

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