SOLUTION: what is the mean and standard deviation of the sampling distribution of proportions respectively, given that n=100 and p= 0.5
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Question 1190937: what is the mean and standard deviation of the sampling distribution of proportions respectively, given that n=100 and p= 0.5 Answer by math_tutor2020(3817) (Show Source):
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p = 0.5 is the population proportion
Each various sample proportion is denoted as
The symbol can be written as "p-hat" or "phat" because the letter p has a hat on top.
The "ph" isn't sounded out as an "f" sound. The "p" is separate from the "hat".
The sample distribution consists of random phat values based on repeated samplings of the population.
In this case, we're sampling 100 individuals to compute the phat values.
The phat distribution will have a mean of p = 0.5 because the phat values will fall on either side of this center. The more data points, the better the picture will come into focus that the center is 0.5
This is all due to the fact the sampling distribution is clustered around the population parameter.
The standard deviation for the phat values isn't as simple unfortunately.
The good news is that the formula isn't too crazy.
sigma = sqrt(p*(1-p)/n)
sigma = sqrt(0.5*(1-0.5)/100)
sigma = sqrt(0.5*0.5/100)
sigma = sqrt(0.25/100)
sigma = sqrt(0.0025)
sigma = 0.05
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