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 = −1.41. Find the p-value p.

z = −1.41H₁: μ < μ₀

p =

2.Easy

A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 10 mL. A sample of 64 bottles has a mean of 122.6 mL. Find the test statistic z for H₀: μ = 120.

μ₀ = 120 mLx̄ = 122.6 mLσ = 10 mLn = 64

z =

3.Medium

A sample of 49 students has a mean score of 506.2 and a sample standard deviation of 15. Find the test statistic t for H₀: μ = 500.

μ₀ = 500x̄ = 506.2s = 15n = 49

t =

4.Medium

Two production lines make the same part. Line 1: a sample of 50 parts has mean length 81 mm, and the line's known standard deviation is 7 mm. Line 2: a sample of 40 parts has mean 78.6 mm, known standard deviation 12 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

n₁ = 50x̄₁ = 81 mmσ₁ = 7 mmn₂ = 40x̄₂ = 78.6 mmσ₂ = 12 mm

z =

5.Hard

A sample of 100 measurements has mean 51.4. The population standard deviation is 15. Find the upper limit U of the 90% confidence interval for the mean.

x̄ = 51.4σ = 15n = 10090%

U =

6.Hard

A sample of 49 measurements has mean 119.3. The population standard deviation is 5. Find the upper limit U of the 95% confidence interval for the mean.

x̄ = 119.3σ = 5n = 4995%

U =

Answer key

1. p = 0.07927
2. z = 2.08
3. t = 2.893
4. z = 1.121
5. U = 53.87
6. U = 120.7

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