An environmentalist group collects a liter of water from each of 45 random locations along a stream and measures the amount of dissolved oxygen in each specimen. the mean is 4.62 milligrams (mg). forty-five water specimens were taken from randomly chosen locations. we assume that dissolved oxygen varies among sampling locations according to a normal distribution with σ = 0.92 mg/l. a statistician tells you that the power of the z test with α = 0.05 against the alternative that the true mean oxygen content is μ = 4.75 mg/l is 0.57.

step 1: to get higher power against the same alternative with the same α, what must we do? decrease the sample size. increase the sample size.

step 2: if we decide to use α = 0.10 in place of α = 0.05, does the power increase or decrease? increase decrease

step 3: if we shift our interest to the alternative μ = 4.5 mg/l and change nothing else, does the power increase or decrease? increase decrease