In 2013, Gallup conducted a poll and found a 90% confidence interval of the proportion of Americans who believe it is the government's responsibility for health care. Give the statistical interpretation.
We often are curious about the population proportion for large sets of data. The population proportion is the proportion of subjects in the population that have a certain trait. The issue is that we often do not have access to the entire population; we are forced to make some statistical inference based on a sample of that population. It is important to interpret the meaning of that inference correctly.
Answer and Explanation:
When we create a confidence interval, we are creating a range of values that we are confident (to some degree) contains the true population proportion for our data.
Say we created a 90% confidence interval for the Americans mentioned in the problem. Let's arbitrarily say that our interval was (0.25, 0.35). What does this mean? This means that we can say with 90% that the true population proportion is somewhere between 0.25 and 0.35.
It is important to note that it is common to misinterpret this interval. The "90%" part of the interval describes the confidence we have in the process for creating the interval. For instance, if 100 different people each took their own sample (of the same sample size) and created their own confidence interval for the population proportion, we would expect that 90 of them "captured" the true population proportion and 10 of them "missed" the true population proportion.
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from Statistics 101: Principles of StatisticsChapter 9 / Lesson 3