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 0.6 of its customers are satisfied. In a random survey of 250 customers, 162 say they are satisfied. Find the test statistic z for H₀: p = 0.6.

p₀ = 0.6n = 250x = 162
z =
2.Easy
−0.93p = ?

A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −0.93. Find the p-value p.

z = −0.93H₁: μ < μ₀
p =
3.Medium
t −2.13102.131

A sample of 16 students has a mean score of 97.2 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 97.2s = 8n = 16
t =
4.Medium
−2.162.16p = ?

The mean of a population is claimed to be 100; the population standard deviation is known to be 15. A random sample of 25 observations has a mean of 106.48. Test H₀: μ = 100 against H₁: μ ≠ 100. Find the p-value p.

μ₀ = 100σ = 15n = 25x̄ = 106.48H₁: μ ≠ μ₀
p =
5.Hard
z −2.57602.576

A sample of 64 measurements has mean 121.2. The population standard deviation is 12. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 121.2σ = 12n = 6499%
L =
6.Hard
H₀H₁μ₀x̄cμ₀ + 2.5α = 0.05βσ = 16, power 95%, n = ?

A one-sided z test at α = 0.05 must detect a shift of the mean of 2.5 units with a power of 95%. The standard deviation is 16. Find the minimum sample size n.

α = 0.05power = 95%δ = 2.5σ = 16zα = 1.645zβ = 1.645
n =

Answer key

  1. 1. z = 1.549
  2. 2. p = 0.1762
  3. 3. t = −1.4
  4. 4. p = 0.03077
  5. 5. L = 117.3
  6. 6. n = 444

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