The U.S. Census Bureau reported that in 2019 the proportion of adult Americans, ages 25 and older, who have a
bachelor's degree or higher is 0.36. t in 2019 the proportion of adult Americans, ages 25 and older, who have a
bachelor's degree or higher is 0.36. Consider the population of all adult Americans, ages 25 and over in 2019 and
define p̂ to be the proportion of people in a random sample from this population who have a bachelor's degree or
higher.
Would p̂ based on a random sample of only 10 people from this population have a sampling distribution that is
approximately normal? Explain why or why not.
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No, the sampling distribution of p̂ based on a random sample of size 10 residents would not be approximately normally distributed because np is less than 10
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Yes, the sampling distribution of p̂ based on a random sample of only 10 people would be approximately normal. This is because the sample size of 10 is reasonably large. According to the Central Limit Theorem, when the sample size is large enough (preferably greater than 30), the sampling distribution of p̂ will be approximately normal, regardless of the shape of the population distribution. In this case, with a sample size of 10, we can assume that the condition for the Central Limit Theorem is approximately met and thus the sampling distribution of p̂ would be approximately normal.
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