# Answer to Question #3643 in Statistics and Probability for abcd

Question #3643

whats the way or role or formula can i usr to find this question<br />

Find the mean, variance and standard deviation of the sampling distribution of the sample proportion, p-hat. <br />

<br />

p = 0.5, n = 250 <br />

<br />

p = 0.1, n = 100 <br />

Find the mean, variance and standard deviation of the sampling distribution of the sample proportion, p-hat. <br />

<br />

p = 0.5, n = 250 <br />

<br />

p = 0.1, n = 100 <br />

Expert's answer

For sampling distribution of the sample proportion, p-hat with parameters p and nmean, variance and standard deviation are calculated by the following formulae:

mean = p

variance = p(1-p)/n

standard deviation = SQUARE_ROOT(variance)

Hence if

1) p = 0.5, n = 250, then

mean = p = 0.5

variance = p(1-p)/n = 0.5 * (1-0.5) / 250 = 0.25/250 = 0.0001

standard deviation = SQUARE_ROOT(variance) = SQUARE_ROOT(0.0001) = 0.01

2) p = 0.1, n = 100, then

mean = p = 0.1

variance = p(1-p)/n = 0.1 * (1-0.1) / 100 = 0.09/100 = 0.0009

standard deviation = SQUARE_ROOT(variance) = SQUARE_ROOT(0.0009) = 0.03

mean = p

variance = p(1-p)/n

standard deviation = SQUARE_ROOT(variance)

Hence if

1) p = 0.5, n = 250, then

mean = p = 0.5

variance = p(1-p)/n = 0.5 * (1-0.5) / 250 = 0.25/250 = 0.0001

standard deviation = SQUARE_ROOT(variance) = SQUARE_ROOT(0.0001) = 0.01

2) p = 0.1, n = 100, then

mean = p = 0.1

variance = p(1-p)/n = 0.1 * (1-0.1) / 100 = 0.09/100 = 0.0009

standard deviation = SQUARE_ROOT(variance) = SQUARE_ROOT(0.0009) = 0.03

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