A machine is set to fill packs with a mean of 75 g; you suspect it underfills. The standard deviation is known to be 6 g. You will weigh a sample of 64 packs and test H₀: μ = 75 against H₁: μ < 75 at α = 0.01. Below which sample mean x̄c will you reject H₀?
A supplier claims that the mean breaking strength of a cable is 75 kN; you suspect it is higher. The standard deviation is known to be 3 kN. You will take a sample of 25 cables and test H₀: μ = 75 kN against H₁: μ > 75 kN at α = 0.10. Above which sample mean x̄c will you reject H₀?
10 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 2.7 and the standard deviation of the differences is 4.5. Find the paired test statistic t for H₀: μd = 0.
12 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 −0.69 and the standard deviation of the differences is 1.5. Find the paired test statistic t for H₀: μd = 0.
In a trial, 55 of 100 patients on treatment A recover, and 92 of 200 patients on treatment B. Using the pooled proportion, find the test statistic z for H₀: p₁ = p₂.
A one-sided z test at α = 0.01 must detect a shift of the mean of 5 units with a power of 95%. The standard deviation is 24. Find the minimum sample size n.
Full step-by-step solutions: practise this topic on examproblems.com.