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?

Group of answer choices

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.

Answer #1

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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students surveyed, 970 admitted to smoking marijuana at least
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hypothesis test to see if the true proportion of high school
students who tried marijuana is now less than 45%. Use
alpha = .01.
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