Question

For today's lab, we will revisit some of the probability ideas and explore the concept of something called a 'confidence interval' using real data from recent General Social Survey (GSS) results. Recall that the GSS is conducted every two years using a randomly selected sample of U.S. adults that live in a household and it asks respondents a variety of questions about sociological issues and attitudes towards various ideas, characteristics, and policies. Because of its design and methodology, the GSS is widely accepted as a random, representative sample of all U.S. adults living in households.

Let's investigate the attitudes of U.S. adults towards the legalization of marijuana. Suppose that, in 2018, 57% of all U.S. adults living in households would say that they think the use of marijuana should be made legal, and suppose that, in 2018, we were able to randomly select one or a few U.S. adults living in a household to ask them their opinion about the legalization of marijuana.

If we randomly selected one U.S. adult living in a household in 2018, what is the probability that they would say they think the use of marijuana should be made legal?

Answer 1

The probability that a randomly selected U.S. adult would support marijuana legalization in 2018 is 57%. Confidence intervals can provide an estimated range that likely includes the true population proportion of support. To calculate a confidence interval, one needs the number of people surveyed and the sample proportion.

Step-by-step explanation:

The student's question pertains to the probability that a randomly selected U.S. adult living in a household in 2018 would say they think the use of marijuana should be made legal, which is given as 57% (0.57 probability). This is a straightforward probability question where the answer is directly provided in the information given. No further computation is necessary for this part of the question.

Now, let's consider the concept of a confidence interval which is often used to estimate the true proportion of a characteristic within a population, in this case, adults living in households. A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

If in a survey conducted by the General Social Survey, 57% of the respondents favored legalization, a confidence interval would allow us to say, with a certain level of confidence (for example, 95% or 99%), what the true proportion is in the entire population. This confidence interval takes into account that different random samples might give slightly different proportions.

Using the example provided and applying it to our student's question, if we wanted to compute a confidence interval estimate for the true proportion of adult U.S. residents who believe marijuana should be legal based on a survey sample, we would need to know the number of people surveyed and the number of those who responded yes. Then we could use a formula to calculate the confidence interval, where the point estimate is the sample proportion, and the margin of error is computed using the critical value from the standard normal distribution (z-score) and the standard error of the proportion.