Question

# Large Sample Proportion Problem. A survey was conducted on high school marijuana use. Of the 2266...

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?

The p-value was below .05, therefore we failed to reject the null hypothesis.

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

Based on a tests statistic that is not in the rejection region for alpha = .01, 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.

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.45
Alternative Hypothesis, Ha: p < 0.45

Rejection Region
This is left tailed test, for α = 0.01
Critical value of z is -2.33.
Hence reject H0 if z < -2.33

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.4281 - 0.45)/sqrt(0.45*(1-0.45)/2266)
z = -2.10

P-value Approach
P-value = 0.0179
As P-value >= 0.01, fail to reject null hypothesis.

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

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