Question

Large Sample Proportion Problem. A survey was conducted on high school marijuana use. Of the 2266 high school students surveyed, 970 admitted to smoking marijuana at 10 years earlier estimated that 45% of the students had tried marijuana. We want to conduct a hypothesis test to see if the true proportion of high school students who tried marijuana is now less than 45%. Use alpha-.01. What is the test statistic for this test? least once. A study done O (45-4237)/SQRT(.4237.5763)/2266) (45-4237)/SQRT((.45*.55)/2266) O(4237- 45)/SQRT(45*.55)/2266) (4237- 45)/SQRT((42375763)/2266) Next Previous Submit C Quiz saved at 2:40pm

Answer 1

Let p denotes the true proportion of high school students who tried marjiuana.

To test against

Here

sample proportion $\hat{p} = \frac{970}{2266} = 0.4237$

and sample size n = 2266

The test statistic can be written as

$z = \frac{(\hat{p}-0.45)}{\sqrt{\frac{0.45*(1-0.45)}{n}}}$ which under H₀ follows a standard normal distribution.

Now,

The value of the test statistic $z_{obs} = \frac{(0.4237-0.45)}{\sqrt{\frac{0.45*(1-0.45)}{2266}}} = \frac{(0.4237-0.45)}{\sqrt{\frac{0.45*0.55}{2266}}}$ (ans)