Question

1. Cigarette and Marijuana Use.  Below are data on cigarette and marijuana use among high school students in Dayton, Ohio.

	Marijuana
Cigarettes	Yes	No
Yes	914	581
No	46	735

1. Write the null and alternative hypotheses for the association between cigarette use and marijuana use. (4 points)
2. How many people would you expect to use both cigarettes and marijuana if the null hypothesis were true? HINT: take a look at the notes for determining expected cell count (2 points)
3. Calculate the p value for the chi squared test of independence for these 2 variables. (2 points)
4. Is cigarette use associated with marijuana use? Explain your answer.  (2 points)

Answer 1

The observed tables with total are given below

Observed
	Mar - Yes	Mar - No	Total
Cig - Yes	914	581	1495
Cig - No	46	735	781
Total	960	1316	2276

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(a) The Hypothesis:

H0: There is no association between cigarettes and Marijuana use.

Ha: There is an association between cigarettes and Marijuana use.

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(b) We want the expected value of Cell 1, which is Yes cigarettes and yes marijuana

The Expected value of a cell = Row total * Column Total / N = 1495 * 960 / 2276 = 630.58

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(c) The p value for test = 642.03 is 0.0000

The test Statistic and The expected value tables are given below

Expected
	Mar - Yes	Mar - No	Total
Cig - Yes	630.58	864.42	1495
Cig - No	329.42	451.58	781
Total	960	1316	2276

Number	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	914	630.58	283.42	80326.91632	127.3858
2	46	329.42	-283.42	80326.91632	243.8434
3	581	864.42	-283.42	80326.91632	92.9258
4	735	451.58	283.42	80326.91632	177.8797
Total					642.0347

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(d) Since p value is very low, we reject the null hypothesis (at all levels of alpha).

Therefore there is sufficient evidence that there is an association between cigarettes and marijuana.

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