A 2016 episode of the NPR program "This American Life" featured a radio show host from Tigerville South Carolina and focused on the divisions among evangelical Christians regarding their support of the then-presidential candidate Donald Trump. We know that these divisions still exist, and suppose you want to survey the people of Tigerville (population: 1.312) to see how many of them support Donald Trump today, and you want to use a simple random sample. (a) An SRS of 150 people is taken and it turns out that 55 support Trump. Estimate the proportion of people in Tigerville that support Trump and give a 95% confidence interval for the true proportion of Trump supporters using your estimate. (b) If 100 simple random samples are taken independently, and 100 such 95% confidence intervals are constructed, what is the probability that all 100 of these intervals will cover the true proportion? Does this number make sense to you? Explain.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.