SOLUTION: A certain school in Southern Africa has a total of 400 learners. The IQ scores of all these learners has a standard deviation of 69 and is normally distributed. A sample of 50 of t

Question 1164665: A certain school in Southern Africa has a total of 400 learners. The IQ scores of all these learners has a standard deviation of 69 and is normally distributed. A sample of 50 of these students had a average IQ score of 174.5. Construct a 98% confidence interval for the true average IQ score of all the learners at this college. Interpret this interval, that is explain in simple English (suitable for publication in a local news paper) what the interval you have constructed above represents.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
half-interval is z(0.99)*sigma/sqrt(n)
=2.328*69/sqrt(50)
=22.72
so the interval is (151.8, 197.2)
We don't know the true mean, but we are very confident, 98% confident, that it lies in the interval we have chosen. Another way of stating this is if we took 100 samples of 50 from this group, 98 of them would have a mean in this interval.
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