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 know facts about the population.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
- 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 know facts about the population.
- Suppose we take an SRS of n=500 people from a population that is 25% Hispanic. How many Hispanic are expected in a given sample?
- What is the standard deviation for the number of Hispanics in a sample?
- Can the Normal approximation to the binomial be used to help make probabilistic statements about samples from this population?
- Determine the
probability that a sample contains 100 or fewer Hispanics under the stated conditions. - Would you suspect undercoverage in a sample with 100 Hispanics? Explain your reasoning.
Given,
n=500
p=0.25
Let X be the random variable that denotes the number of Hispanics in a sample.
Therefore X~Binomial(n=500,p=0.25)
1. The required no. of Hispanic expected in a given sample is obtained as-
2. The required standard deviation for the number of Hispanic in the sample is obtained as-
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