Question

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.

Assuming that it was 57% of all U.S. adults that believed marijuana should be made .75 legal in 2018 , what is the mean (or average) sample percentage who believe that marijuana should be made legal that we would expect to see when we take a random sample of the same size the GSS took?

Answer 1

The mean sample percentage of U.S. adults favoring marijuana legalization, based on random samples, is expected to be close to the population percentage of 57%, as dictated by the law of large numbers.

If 57% of all U.S. adults believe that marijuana should be made legal, and we take a random sample, the mean or average sample percentage is expected to be very close to the population percentage due to the law of large numbers.

The law of large numbers states that as the size of a sample increases, the sample mean approaches the population mean. In this scenario, assuming a sufficiently large random sample is taken, the mean sample percentage of those who believe marijuana should be made legal will converge toward the population percentage of 57%.

For example, if the General Social Survey (GSS) took a random sample of U.S. adults living in households in 2018, the average of the sample percentages obtained from different random samples is likely to be close to 57%. The larger the sample size, the more precise our estimate becomes.

In summary, the mean sample percentage of U.S. adults believing marijuana should be made legal, based on random samples similar to those taken by the GSS, is expected to be approximately 57%, reflecting the population proportion.