Question

which scenarios use the correct mean, population (μ), or sample (x̄) to represent the calculation? check all that apply. a café owner wants to determine the average pay per week for all his employees. the mean should be calculated using population (μ). a scientist wants to determine how nitrogen levels affect the average height of some of the bean sprouts grown in his greenhouse. the mean should be calculated using population (μ). a psychology student surveys dr. kohls 10 a.m. english students about the number of hours they spend studying each week. the mean should be calculated using sample (x̄). a cattle rancher weighs each of his cattle every six months. he calculates the average weight. the mean should be calculated using population (μ). a running shoe distributor wants to know the average monthly inventory of a particular brand of shoe. he compiles the data from all the stores. the mean should be calculated using sample (x̄).

Explanation:

• Option 1: The café owner wants the average for all employees (the entire population), so using population mean ($\mu$) is correct.
• Option 2: The scientist is looking at only some bean - sprouts (a sample), so should use sample mean ($\bar{x}$), not population mean.
• Option 3: The psychology student is surveying Dr. Kohl's 10 a.m. English students (a sample of all students), so using sample mean ($\bar{x}$) is correct.
• Option 4: The cattle rancher weighs each of his cattle (the entire population of his cattle), so using population mean ($\mu$) is correct.
• Option 5: The running - shoe distributor compiles data from all stores (the entire population of relevant stores for that brand), so should use population mean ($\mu$), not sample mean.

Answer:

A. A café owner wants to determine the average pay per week for all his employees. The mean should be calculated using population ($\mu$).
C. A psychology student surveys Dr. Kohl's 10 a.m. English students about the number of hours they spend studying each week. The mean should be calculated using sample ($\bar{x}$).
D. A cattle rancher weighs each of his cattle every six months. He calculates the average weight. The mean should be calculated using population ($\mu$).