Question

The concept of sampling error is discussed in the section Understanding the Margin of Sampling Error in the middle of page 4 in the document New York Times Polling Standards (pdf). The third paragraph in this section is discussing the sampling distribution of p̂, where p̂ is the sample proportion of items in a sample that has the characteristic of interest.

It may assist you in answering the following questions to first verify the statement made in the last sentence of the third paragraph: "And 95 out of those 100 separate poll measures would be between 37% and 43%". Recall that the population proportion p is .40 and n = 1000.

QUESTION: The sample proportions 38% (.38) and 42% (.42) are mentioned in the third paragraph. For a sample of size n = 1000, what is P(.38 ≤ p̂ ≤ .42) when the population proportion p is .40?

Answer 1