A youth prevention organization is examining the effect of peer pressure on the

Question

A youth prevention organization is examining the effect of peer pressure on the decision of teenagers to smoke. A survey of 97 teenagers, ages 11 to 17 years who smoked in the last 30 days, was conducted. The random sample consisted of 25 teenagers who said all/most of their friends smoke, 40 who said some of their friends smoke, and 32 who said none of their friends smoke. The results are shown in the figure. At alpha = 0.01, can you support the organization's claim that the proportion of teens who decide to smoke is lower when none of their friends smoke? How Friends Affect Youth Smoking Percentage of 11 -17-year-olds who smoked a cigarette at least once in the past 30 days

Explanation / Answer

Null Hypothesis, HO : Proportion of teens who decide to smoke is independent of how many of their friends smoke

Alternate Hypothesis, H1 : Proportion of teens who decide to smoke is independent of how many of their friends smoke

Let’s define events A = All/Most friends smoke

B = Some friends smoke

C= No friends smoke

X= The person surveyed smokes

P(X/A) = 25/97 ( Weight = 1)

P(X/B) = 40/97 (Weight = 0..5)

P(X/C) = 32/97 (Weight = 1)

P(X&A,B) = P(X/A) (= 25/97) + P(X/B)/2 (= 20/97)

= 45/97

P(X&C) = 1 – 45/97 = 52/97 = 53.61

Thus the null hypothesis is rejected.

We support the organizations claim that proportion of teens who decide to smoke is lower when none of their friends smoke.

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