Explain the general process we would like to use to evaluate whether the sample mean hours we observed for our class provide convincing evidence that the population of students as a whole average less than 8 hour of sleep on a typical night, pretending we had collected a random sample from all students at your school.
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To determine whether we have convincing evidence that students at your school average less than 8 hours (i.e.,
< 8), we will assume that
= 8, see what are typical values for the sample mean for random samples of the same size from such a population, and then decide whether or not the value of the sample mean we actually found for our class is consistent with this random sampling variability. The problem is, we don't know anything else about the population, like the shape and the standard deviation.