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
z −1.9601.96

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 8 mL. A sample of 36 bottles has a mean of 53.87 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 53.87 mLσ = 8 mLn = 36
z =
2.Easy
μ₀x̄c = ?α = 0.05

A machine is set to fill packs with a mean of 500 g; you suspect it underfills. The standard deviation is known to be 4 g. You will weigh a sample of 36 packs and test H₀: μ = 500 against H₁: μ < 500 at α = 0.05. Below which sample mean x̄c will you reject H₀?

μ₀ = 500 gσ = 4 gn = 36α = 0.05
x̄c = g
3.Medium
t −2.13102.131

A sample of 16 students has a mean score of 107.2 and a sample standard deviation of 12. Find the test statistic t for H₀: μ = 100.

μ₀ = 100x̄ = 107.2s = 12n = 16
t =
4.Medium
−2.0642.064t = ?df = 24

Two teaching methods are compared. Group 1: 19 students, mean score 71.5, standard deviation 7.5. Group 2: 7 students, mean score 74.1, standard deviation 7. Assume equal population variances and use the pooled two-sample t test. Find the test statistic t for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (group 1 minus group 2).

n₁ = 19x̄₁ = 71.5s₁ = 7.5n₂ = 7x̄₂ = 74.1s₂ = 7
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 4α = 0.01βσ = 22, power 95%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 4 units with a power of 95%. The standard deviation is 22. Find the minimum sample size n.

α = 0.01power = 95%δ = 4σ = 22zα = 2.326zβ = 1.645
n =
6.Hard
σ = 20, n = ?x̄ − Ex̄ + Ex̄E = 295%

How large must a sample be so that the 95% confidence interval for a mean has a margin of error of at most 2? The standard deviation is 20. Find the smallest sample size n.

σ = 20E = 295%
n =

Answer key

  1. 1. z = 2.902
  2. 2. x̄c = 498.9 g
  3. 3. t = 2.4
  4. 4. t = −0.797
  5. 5. n = 478
  6. 6. n = 385

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