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 120 mL on average. The standard deviation is known to be 4 mL. A sample of 25 bottles has a mean of 121.9 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 121.9 mLσ = 4 mLn = 25
z =
2.Easy
μ₀x̄c = ?α = 0.01

A supplier claims that the mean breaking strength of a cable is 75 kN; you suspect it is higher. The standard deviation is known to be 12 kN. You will take a sample of 36 cables and test H₀: μ = 75 kN against H₁: μ > 75 kN at α = 0.01. Above which sample mean x̄c will you reject H₀?

μ₀ = 75 kNσ = 12 kNn = 36α = 0.01
x̄c = kN
3.Medium
−2.2622.262t = ?df = 9

10 employees take a typing test before and after a training course. For each person the difference d = after − before (words per minute) is recorded. The mean difference is 1.9 and the standard deviation of the differences is 6. Find the paired test statistic t for H₀: μd = 0.

n = 10d̄ = 1.9sd = 6
t =
4.Medium
−2.0642.064t = ?df = 24

Two teaching methods are compared. Group 1: 19 students, mean score 84.5, standard deviation 8. Group 2: 7 students, mean score 87.3, standard deviation 8. 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 = 84.5s₁ = 8n₂ = 7x̄₂ = 87.3s₂ = 8
t =
5.Hard
H₀H₁μ₀x̄cμ₀ + 2α = 0.01βσ = 15, power 80%, n = ?

A one-sided z test at α = 0.01 must detect a shift of the mean of 2 units with a power of 80%. The standard deviation is 15. Find the minimum sample size n.

α = 0.01power = 80%δ = 2σ = 15zα = 2.326zβ = 0.842
n =
6.Hard
z −1.64501.645

A sample of 64 measurements has mean 74.8. The population standard deviation is 15. Find the lower limit L of the 90% confidence interval for the mean.

x̄ = 74.8σ = 15n = 6490%
L =

Answer key

  1. 1. z = 2.375
  2. 2. x̄c = 79.65 kN
  3. 3. t = 1.001
  4. 4. t = −0.7916
  5. 5. n = 565
  6. 6. L = 71.72

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