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 = −1.75. Find the p-value p.

z = −1.75H₁: μ < μ₀

p =

2.Easy

A company claims that a proportion of 0.75 of its customers are satisfied. In a random survey of 150 customers, 103 say they are satisfied. Find the test statistic z for H₀: p = 0.75.

p₀ = 0.75n = 150x = 103

z =

3.Medium

A sample of 49 students has a mean score of 74 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 75.

μ₀ = 75x̄ = 74s = 5n = 49

t =

4.Medium

7 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 1.58 and the standard deviation of the differences is 1.9. Find the paired test statistic t for H₀: μ_d = 0.

n = 7d̄ = 1.58s_d = 1.9

t =

5.Hard

In a trial, 60 of 300 patients on treatment A recover, and 24 of 200 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

x₁ = 60n₁ = 300x₂ = 24n₂ = 200

z =

6.Hard

A one-sided z test at α = 0.05 must detect a shift of the mean of 4 units with a power of 95%. The standard deviation is 19. Find the minimum sample size n.

α = 0.05power = 95%δ = 4σ = 19z_α = 1.645z_β = 1.645

n =

Answer key

1. p = 0.04006
2. z = −1.791
3. t = −1.4
4. t = 2.2
5. z = 2.344
6. n = 245

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