SOLUTION: According to the US Census Bureau, roughly 14.5% of individuals are living below the poverty level. Suppose a random sample of 500 individuals was taken. a. Describe the samplin

Question 288143: According to the US Census Bureau, roughly 14.5% of individuals are living below the poverty level. Suppose a random sample of 500 individuals was taken.
a. Describe the sampling distribution of p-hat, the sample proportion of individuals living below the poverty level.
1. The mean of p-hat is:_________
2. The standard error of p-hat is:_________
3. In a random sample of 500 individuals, find the probability that no more than 10% are living below the poverty level.
What is the probability that a random sample of 500 individuals results in 80 or more having an advanced degree?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
According to the US Census Bureau, roughly 14.5% of individuals are living below the poverty level.
Suppose a random sample of 500 individuals was taken.
a. Describe the sampling distribution of p-hat, the sample proportion of individuals living below the poverty level.
1. The mean of p-hat is: 14.5% according to the Central Limit Theorem
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2. The standard error of p-hat is: sqrt(0.145*0.855/500) = 0.0157 according to CLT
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3. In a random sample of 500 individuals, find the probability that no more than 10% are living below the poverty level.
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Find the z-value that has a left tail of 10%: z = -1.2816..
Find the x-value associated with z = -1.2816
x = -1.2816*0.0157+ 0.145
x = 0.1249
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Cheers,
Stan H.

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