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 H_a: 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

Given that, the null and alternative hypotheses are,

H0 : p = 0.173 versus Ha : p < 0.173

sample size ( n ) = 80

Here, np = 80 * 0.173 = 13.84 > 10 and

n(1-p) = 80 * (1-0.173) = 66.16 > 10

Therefore, the sample size condition for conducting a hypothesis test for a population proportion is satisfied.

Yes, because (80)(.173) and (80)(1 ‑ 0.173) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions