Question 1170269: A random sample of 732 judges found that 405 were introverts. Construct a 95%
confidence interval for the proportion. Interpret the meaning of the confidence interval.
Justify your use of a confidence interval based on a normal distribution for data
regarding proportions that are normally following a binomial distribution
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 405/732=0.553
half-interval for 95% CI is z*sqrt(p*(1-p)/n)=1.96* sqrt (0.553*0.447/732)
=0.036
95CI is (0.517, 0.589)
We don't know the true proportion of judges who are introverts, but we are highly confident the proportion lies within the interval.
If we constructed 100 such intervals with this sample size, 95 of them would contain the true proportion. We wouldn't know, however, which 95.
np and n(1-p) are both greater than 10. So normal distribution may be used.
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