Question

Legalization of marijuana, Part 1. The 2010 General Social Survey asked 1,259 US res- idents: "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. (a) 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?

Answer 1

see below

Explanation:

(a) 48% is a sample statistic because it's based on the responses of 1,259 US residents. It's used to estimate a population parameter.

(b) We can calculate a 95% confidence interval for the proportion of US residents who support marijuana legalization. This interval provides a range, and we can be 95% confident that the true proportion falls within this range.

(c) The confidence interval calculation assumes the data follows a normal distribution. To use this method, we need a sufficiently large sample size, which is met in this case.

(d) To justify the news piece's statement that a majority of Americans support marijuana legalization, we need to check if the confidence interval includes values above 50%. If it does, then it supports the statement.