The General Social Survey (GSS) has been collecting demographic, behavioral, and

Question

The General Social Survey (GSS) has been collecting demographic, behavioral, and attitudinal information since 1972 to monitor changes within the US and to compare the US to other nations. Support for the legalization of marijuana in the US is shown for 2010 and in 2016 in the following table: Year FavorOppose Total 2010 603 656 1259 2016 1126 717 1843 Part A: Find a 95% confidence interval for the change in the proportion supporting marijuana legalization from 2010 to 2016. Use Python for all computations and show your work. Part B: Is it likely that the proportion supporting marijuana legalization changed between 2010 and 2016? Justify your conclusion using the ideas of statistical inference and your results from Part A.

Explanation / Answer

Part A

Let p1 and p2 represent the proportion supporting marijuana legalization in 2010 and 2016, respectively,

we have p1 = 1126/1843 = 0.612 and p2 = 603/1259 = 0.479

The sample sizes are both large, so it is reasonable to use a normal distribution. For 95% confidence the standard normal endpoint is z ? = 1.96. This gives

(p1 ? p2) ± z ? X sqrt [p1(1 ? p1) / n1 + p2 (1 ? p2) / n2]

(0.612-0.479) ± 1.96*sqrt[0.612(1-0.612)/1843 + 0.479(1-0.479)/1259]

0.133 ± 0.035

0.098 to 0.168

We are 95% sure that, between 2010 and 2016, the percent change in support of the marijuana legalization is between an increase of 9.8% and an increase of 16.8%.

Part B

Since a difference of zero (no change) is not within this interval, it is plausible that there have been change in support or opposition to the marijuana legalization in this 6-year period.

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