6.12 Legalization of marijuana, Part I. The 2010 General Social Survey asked 1,2

Question

6.12 Legalization of marijuana, Part I. The 2010 General Social Survey asked 1,259 US residents: Do you think the use of marijuana should be made legal, or not?" 48% of the respondents said it should be made legal.

(a) Is 48% a sample statistic or a population parameter? Explain.

(b) Construct a 95% confidence interval for the proportion of US residents who think marijuana should be made legal, and interpret it in the context of the data.

(c) A critic points out that this 95% confidence interval is only accurate if the statistic follows a normal distribution, or if the normal model is a good approximation. Is this true for these data? Explain.

(d) A news piece on this survey's findings states, "Majority of Americans think marijuana should be legalized." Based on your confidence interval, is this news piece's statement justified?

Explanation / Answer

a. Here it is given that n=1259 and so 48% is statistics

b. For 95% z is 1.96

So E=z*sqrt(p(1-p)/n)=1.96*sqrt(0.48*0.52/1259)=0.03

Hence CI=p+/-E=(0.45,0.51)

c. np=1259*0.48=604.32>10

d. Yes it is justified

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