Question 625817: It is known that the population mean for the verbal section of the SAT is 500 with a standard deviation
of 100. In 2006, a sample of 400 students taking SAT whose family income was between $70,000 and
$80,000 had a verbal SAT score of 511. Find the 99% confidence interval for this group.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! population mean is equal to 500
population standard deviation is equal to 100
sample of 400 students has a sample mean of 511.
sample mean standard deviation = population standard deviation / square root of sample size.
this becomes;
sample mean standard deviation = 100 / sqrt(400) which is equal to 5.
99% confidence level is achieved within +/- 2.576 standard deviations.
2.576 standard deviations * 5 is equal to +/- 12.88
this means that, at 99% percent confidence level, the sample mean of 511 infers a population mean between 498.12 and 523.88
this also means that, if you took many samples of 400 students each, 99% of the time your sample mean would be between 498.12 and 523.88.
that's my understanding of what they are looking for here.
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