Question 1002371: About 69% of young adult Internet users (ages 18 to 29) use social-networking sites. Suppose that a sample survey contacts an SRS of 1900 young adult Internet users and calculates the proportion p̂ in this sample who use social-networking sites. (Enter your means to two decimal places and round your standard deviations to four decimal places.)
(a) What is the approximate distribution of p̂?
mean:
standard deviation:
b) If the sample size were 6000 rather than 1900, what would be the approximate distribution of p̂?
mean:
standard deviation:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The point estimate of p, or phat=0.69
mean is 0.69 and sd is sqrt{ (0.69)(0.31/1900}
The standard error is 0.0106.
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sample size of 6000 doesn't change the mean or point estimate, but the SE is much less, or 0.00597.
The standard error is the standard deviation of the sampling distribution. It is dependent upon the probability and the sample size. The mean of the sampling distribution is the probability obtained, or the point estimate. Different samples will give different means, but whatever is obtained from the sample itself it the single best estimate and called the point estimate.
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