SOLUTION: A poll was done where 450 adults were randomly surveyed. 35 % said they were working hard at their jobs and hoped to get a promotion. Calculate and interpret a 95 % confidence in

Question 1157867: A poll was done where 450 adults were randomly surveyed. 35 % said they were working hard at their jobs and hoped to get a promotion. Calculate and interpret a 95 % confidence interval for the proportion of adults who said they were working hard and hoped for a promotion.
Give the lower and upper limits of the 95 % confidence interval for this example.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The half-interval for CI=95% is z(1.96)*sqrt(p(1-p)/n)
that is added and subtracted to the point estimate of 35%
SE=sqrt(.35*.65/450)=0.0005056=0.0225
1.96*0.0225=0.0440
95% confidence interval for the true proportion is (0.306, 0.394)
Note: this will be different on a calculator, because 35% of 450 is not an integer, so one has to use 157/450 or 158/450, giving a slightly different interval from 157.5/450

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