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 least once.  A study done 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 conclusion for this test?

Based on a tests statistic that is not in the rejection region for alpha = .01, we failed to reject the null hypothesis.

The p-value was below .01, therefore we failed to reject the null hypothesis.

Based on a p-value less than .01, we would reject the null hypothesis and conclude the rate is now lower than 45.

The p-value was below .05, but not .01, therefore we failed to reject the null hypothesis.

Answer 1

Here claim is that  true proportion of high school students who tried marijuana is now less than 45%.

Which means hypothesis is vs

As we have n=2266 which is sufficient large so we will use z distribution

Test statistics is

Where and

So test statistics is

P value is

The z-critical value for a left-tailed test, for a significance level of ?=0.01 is

zc?=?2.33

Graphically

As we see that P value is greater than alpha=0.01 we fail to reject the null hypothesis

Also we see that z statistics is not in the rejection region we fail to reject the null hypothesis

So answer is

Based on a tests statistic that is not in the rejection region for alpha = .01, we failed to reject the null hypothesis.