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

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = 1.01. Find the p-value p.

z = 1.01H₁: μ ≠ μ₀

p =

2.Easy

A machine is supposed to fill bottles with 50 mL on average. The standard deviation is known to be 10 mL. A sample of 64 bottles has a mean of 47.25 mL. Find the test statistic z for H₀: μ = 50.

μ₀ = 50 mLx̄ = 47.25 mLσ = 10 mLn = 64

z =

3.Medium

Two teaching methods are compared. Group 1: 5 students, mean score 116, standard deviation 4. Group 2: 7 students, mean score 135.7, standard deviation 12. 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 = 5x̄₁ = 116s₁ = 4n₂ = 7x̄₂ = 135.7s₂ = 12

t =

4.Medium

A sample of 49 students has a mean score of 197.9 and a sample standard deviation of 8. Find the test statistic t for H₀: μ = 200.

μ₀ = 200x̄ = 197.9s = 8n = 49

t =

5.Hard

A sample of 64 measurements has mean 44.6. The population standard deviation is 15. Find the lower limit L of the 99% confidence interval for the mean.

x̄ = 44.6σ = 15n = 6499%

L =

6.Hard

A sample of 64 measurements has mean 73.2. The population standard deviation is 8. Find the upper limit U of the 95% confidence interval for the mean.

x̄ = 73.2σ = 8n = 6495%

U =

Answer key

1. p = 0.3125
2. z = −2.2
3. t = −3.492
4. t = −1.837
5. L = 39.77
6. U = 75.16

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