Knowing What You Need to Run a z-Test
Conducting a hypothesis test is somewhat like doing detective work. Every population has a mean, and it’s usually unknown. Many people claim that they know what it is; others assume that it hasn’t changed from a past value; and in many cases, the population mean is supposed to follow certain specifications.
Your modus operandi is to challenge or test that value of the population mean that’s already assumed, given, or specified and use data as your evidence. That’s what hypothesis testing is all about.
Figure out what you need to know to run a z-test in the following problem.
Dr. Thompson, a health researcher, claims that a teenager in the United States drinks an average of 30 ounces of sugary carbonated soda per day.
A high-school statistics class decides to test this claim and is open to soda consumption being, on average, either higher or lower than the claimed 30 ounces per day. They conduct a random survey of 15 of their classmates and find self-reported soda consumption is, on average, 25 ounces per day.
What additional information would you need to run a z-test to determine whether the students in this school drink significantly more or less soda than Dr. Thompson claims is consumed by U.S. teens in general?
Answer: the population standard deviation and a statement that soda consumption is normally distributed among U.S. teens
To run a z-test to see whether a sample mean differs from a population mean, you need the population standard deviation; you also need to know either that the characteristic of interest is normally distributed in the population or that the sample size is at least n = 30.
Because the sample is small (n = 15), you need to know that soda consumption is normally distributed among U.S. teens and the population standard deviation of soda consumption.
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