IMathAS-libretexts

Hint 1 Hint 2 Hint 3

According to the Center for Disease Control (CDC), roughly 21.5% of all high-school seniors in the United States. have used marijuana. (Comments: The data were collected in 2002. The figure represents those who smoked during the month prior to the survey, so the actual figure might be higher). A sociologist suspects that the rate among African-American high school seniors is lower, and wants to check that. In this case, then,

Claim 1: The rate of African-American high-school seniors who have used marijuana is 21.5% (same as the overall rate of seniors).
Claim 2: The rate of African-American high-school seniors who have used marijuana is lower than 21.5%.

To check his claim, the sociologist chooses a random sample of 375 African-American high school seniors, and finds that 16.5% of them have used marijuana.

In order to assess the evidence, we need to ask:

how likely it is that the true rate (i.e., the rate among all African-American high-school seniors) is 21.5%.
how likely it is that the true rate is lower than 21.5%.
how likely it is that in a sample of 375 we'll find that as low as 16.5% have used marijuana.
how likely it is that in a sample of 375 we'll find that as low as 16.5% have used marijuana, when the true rate is actually 21.5%.

License