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Undercoverage is a problem that occurs in surveys when some groups in the population are underrepresented in the sampling frame used to select the sample. We can check for undercoverage by comparing the sample with known facts about the population. Suppose we take an SRS of n = 500 people from a population that is 25% Hispanic
a) Would a sample mean with 100 Hispanic people be different from the population mean? Give the p-value and explain your reasoning.
b) What is the confidence interval for the sample mean of 100?
c) Does the confidence interval agree with your p-value, explain your reasoning.
d) Would you suspect undercoverage in a sample with 100 Hispanics? Explain your reasoning.
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