Hypothesis tests & confidence intervals worksheet with answers

A z test of H₀: μ = μ₀ against H₁: μ < μ₀ gives the test statistic z = −2.2. Find the p-value p.

A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 15 mL. A sample of 49 bottles has a mean of 504.5 mL. Find the test statistic z for H₀: μ = 500.

13 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 0.44 and the standard deviation of the differences is 1. Find the paired test statistic t for H₀: μ_d = 0.

Two production lines make the same part. Line 1: a sample of 40 parts has mean length 59.5 mm, and the line's known standard deviation is 18 mm. Line 2: a sample of 50 parts has mean 67.1 mm, known standard deviation 5 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

In a trial, 42 of 120 patients on treatment A recover, and 78 of 300 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.

A sample of 49 measurements has mean 198.6. The population standard deviation is 10. Find the upper limit U of the 95% confidence interval for the mean.