Hypothesis tests & confidence intervals worksheet with answers

A z test of H₀: μ = μ₀ against H₁: μ > μ₀ gives the test statistic z = 0.82. Find the p-value p.

A company claims that a proportion of 0.3 of its customers are satisfied. In a random survey of 100 customers, 22 say they are satisfied. Find the test statistic z for H₀: p = 0.3.

Two production lines make the same part. Line 1: a sample of 80 parts has mean length 70.5 mm, and the line's known standard deviation is 12 mm. Line 2: a sample of 60 parts has mean 68.8 mm, known standard deviation 16 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

11 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 −3.09 and the standard deviation of the differences is 3.2. Find the paired test statistic t for H₀: μ_d = 0.

A one-sided z test of H₀: μ = 100 against H₁: μ > 100 is done at α = 0.10 with a sample of 25; the standard deviation is known to be 7.5. In reality the mean is 101.8. Find the probability of a Type II error β in percent.

A sample of 64 measurements has mean 118.1. The population standard deviation is 10. Find the lower limit L of the 99% confidence interval for the mean.