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 _____.
A) 500; [501.2, 520.8]
B) 500; [490.2, 509.8]
C) 511; [501.2, 520.8]
D) 511; [490.2, 509.8]

Question

Quizplus · Accepted Answer

The point estimate of the mean is the sample mean, which is given as 511 in the problem. 
To find the 95% confidence interval, we can use the formula: 
Confidence Interval = sample mean ± (critical value)*(standard error) 
The critical value for a 95% confidence interval with a sample size of 400 is approximately 1.96. 
The standard error can be calculated as the standard deviation of the population divided by the square root of the sample size: 
standard error = 100/√400 = 5 
Plugging in all the values, we get: 
Confidence Interval = 511 ± 1.96*5 
Confidence Interval = [501.2, 520.8] 
Therefore, the answer is (C) 511; [501.2, 520.8].

It Is Known That the Population Mean for the Verbal