Hypothesis tests & confidence intervals worksheet with answers

A company claims that a proportion of 0.6 of its customers are satisfied. In a random survey of 200 customers, 133 say they are satisfied. Find the test statistic z for H₀: p = 0.6.

A machine is supposed to fill bottles with 120 mL on average. The standard deviation is known to be 5 mL. A sample of 49 bottles has a mean of 121.7 mL. Find the test statistic z for H₀: μ = 120.

A sample of 36 students has a mean score of 99.25 and a sample standard deviation of 5. Find the test statistic t for H₀: μ = 100.

Two teaching methods are compared. Group 1: 5 students, mean score 90.5, standard deviation 2.5. Group 2: 9 students, mean score 87.5, standard deviation 11. 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 one-sided z test of H₀: μ = 80 against H₁: μ > 80 is done at α = 0.05 with a sample of 100; the standard deviation is known to be 20. In reality the mean is 82. Find the power 1 − β of the test in percent.

How large must a sample be so that the 90% confidence interval for a mean has a margin of error of at most 3? The standard deviation is 12. Find the smallest sample size n.