Question

According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of 8th graders in 2010 had used marijuana at some point in their lives. A school official hopes to show the percentage is lower in his district, testing H0: p=0.173 versus Ha: p>0.173.

The health department for the district uses anonymous random sampling and finds that 10% of 80 eighth graders surveyed had used marijuana.

Is the sample size condition for conducting a hypothesis test for a population proportion satisfied?

Answer 1

solution

$$n=80, p=0.173$$

Since:

$$np = 80*0.173 = 13.84$$ $$n(1-p)=80*(1-0.173)=66.16$$

Both $np$ and $n(1-p)$ are greater than 10 meaning the distribution of sample proportions can be modelled by the normal distribution. Hence the sample size is sufficient for the hypothesis using normal Z tables.