#214 A random sample of 500 students from a large

A random sample of 500 students from a large - Math

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Free Chegg Question

A random sample of 500 students from a large university was interviewed about the high school SAT scores (X) and their current university GPAS (Y). The students wer classified into two groups: those with SAT scores greater than or equal to the nationa average (X 1) and those with SAT scores below the national average (X = 0). Th average GPA was calculated for each group.

(a) What estimator does the table provide for the population mean GPA of student with SAT scores below the national average? No of observations Average GPA SAT below average 175 2.8 SAT above average 325 3.2

(b) Is this estimator a random variable?

(c) What is the realized value of this estimator, i.e. what is the estimate of the mea GPA of students with SAT scores below the national average?

(d) Is this estimate a random variable?

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Free Chegg Answer

a) The estimator that the table provides is the "sample mean" or "sample average". The sample mean / average is always an unbiased estimator of population mean/average. Therefore in the table, the sample mean GPA of students with SAT scores below average is the estimator of the population mean GPA of students with SAT score below average.

b) Estimator , i.e., sample mean, is the average value of sample observations, which in turn is a random variable. Therefore this estimator (sample mean) is a random variable too.

c) The realised value of sample mean is 2.8. (It is given in table). This is the estimate of estimator.

d) The estimate of estimator is a fixed value (calculated/computed). Therefore it is not a random variable