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 a verbal SAT score of 511. The point estimate of the mean for this group is ______ .

A) 500
B) 511
C) 493.55, 506.45
D) 504.55, 517.45

Answer 1

The point estimate of the mean is the sample mean
`(\(\bar{x}\))`. In this case, the sample mean is given as 511. Therefore, the correct answer is: B) 511

In 2006, a sample of 400 students with family incomes between $70,000 and $80,000 took the SAT verbal section.

The population mean for the SAT verbal section is 500 with a standard deviation of 100. The sample mean (point estimate) for this group is 511. This suggests that, on average, students in this income bracket scored slightly higher than the overall population mean.

The confidence interval for the true population mean can be calculated as ±1.96 times the standard error of the mean. However, the options provided do not include a confidence interval, so the point estimate, which is the sample mean of 511, is the best representation of the sample data. Therefore, the correct answer is B) 511.