Question

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 whose family income was between $70,000 and $80,000 had an average verbal SAT score of 511. The point estimate of the mean for this group is _____ and the 95 percent confidence interval for this group is _____.

Answer 1

Answer

given,

SAT is 500 with a standard deviation of 100.

a sample of 400 students whose family income was between $70,000 and $80,000 had an average verbal SAT score of 511.

sample mean = $\dfrac{standard\ deviation}{\sqrt{n}}$

                      = $\dfrac{100}{\sqrt{400}}$

                      = 5

95% confidence level is achieved within +/- 1.960 standard deviations.

1.960 standard deviations  x  5 is equal to +/- 9.8

confidence interval = 511 - 9.8   ---  511 + 9.8

                                = 501.2-----520.8