Question

Climate Change In July 2015, a poll asked a random sample of 1,236 registered voters in Iowa whether they agree or disagree that the world needs to do more to combat climate change. \({ }^{26}\) The results show that \(65 \%\) agree, while \(25 \%\) disagree and \(10 \%\) don't know. (a) What is the sample? What is the intended population? (b) Is it reasonable to generalize this result and estimate that \(65 \%\) of all registered voters in Iowa agree that the world needs to do more to combat climate change?

Short answer

(a) The sample is the 1,236 registered voters in Iowa polled in July 2015. The intended population is all registered voters in Iowa. (b) Considering the sample is random, it is reasonably justifiable to generalize this result and estimate that \(65 \%\) of all registered voters in Iowa agree that the world needs to do more to combat climate change. However, it's important to bear in mind that this generalization comes with some level of uncertainty due to potential sampling error or bias.

Step-by-step solution

Identify the Sample and Population

The sample in a statistical study is the set of subjects or objects that are being observed or measured. In this case, the sample is the 1,236 registered voters in Iowa who were asked whether they agree or disagree that the world needs to do more to combat climate change. The population in a statistical study refers to the total set of objects or subjects that we are interested in studying. Here, the intended population is all registered voters in Iowa.

Evaluate Reasonability of the Generalization

It's necessary to consider whether it's reasonable to generalize this result and estimate that \(65 \%\) of all registered voters in Iowa agree that the world needs to do more to combat climate change. The reasonableness of such a generalization depends on the representativeness of the sample taken. Since the sample is random, we can assume it's reasonably representative of the population. However, it's important to note that there will always be some level of uncertainty when it comes to generalizing from a sample to a larger population, as it's entirely possible that sample results could be influenced by sampling error or bias.