SOLUTION: 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 wa
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-> SOLUTION: 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 wa
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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.
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.
