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

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 =
`(standard\ deviation)/(√(n))`

=
`(100)/(√(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