Question 1193053: According to a Boston Globe story, only about 1 in 6 Americans have blue eyes, whereas in 1900 about half had blue eyes. (Source: Data from The Boston Globe October 17, 2006.)
a. For a random sample of 100 living Americans, find the mean and standard deviation of the proportion that have blue eyes.
b. In a course you are taking with 100 students, half of the students have blue eyes. Would this have been a surprising result if the sample were a random sample of Americans? Answer by finding how many standard deviations that sample result falls from the mean of the sampling distribution of the proportion of 100 students who have blue eyes.
c. In part b, identify the population distribution, the data distribution, and the sampling distribution of the sample proportion.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The mean is np=100(1/6)=16.67 people
variance is np*(1-p)=(100/6)*(5/6)=500/36 people ^2; the 5/6 is 1-p
sd is sqrt (V)=sqrt(500/6)=3.727 people.
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This would be a surprising finding with 50 people's being 8.94 sd above the expected value.
The population distribution is mean=p (0.167)
The data distribution is mean 0.5,
The difference (for z testing ) is( phat-p )=z*sqrt (p*(1-p)/n);note the parameter tested against is under the radical.
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