Hypothesis tests & confidence intervals worksheet with answers

A z test of H₀: μ = μ₀ against H₁: μ ≠ μ₀ gives the test statistic z = −2.17. Find the p-value p.

A machine is supposed to fill bottles with 100 mL on average. The standard deviation is known to be 5 mL. A sample of 49 bottles has a mean of 100.5 mL. Find the test statistic z for H₀: μ = 100.

Two production lines make the same part. Line 1: a sample of 30 parts has mean length 76.5 mm, and the line's known standard deviation is 7 mm. Line 2: a sample of 30 parts has mean 71.6 mm, known standard deviation 7 mm. Find the test statistic z for H₀: μ₁ = μ₂, taking the difference as x̄₁ − x̄₂ (line 1 minus line 2).

Two teaching methods are compared. Group 1: 22 students, mean score 78, standard deviation 5. Group 2: 9 students, mean score 75.8, standard deviation 3. 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).

A sample of 16 measurements has mean 79.8. The population standard deviation is 8. Find the lower limit L of the 90% confidence interval for the mean.

In a trial, 60 of 120 patients on treatment A recover, and 138 of 250 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.