ASU is concerned about the retention rate among its students, i.e. percentage of ASU students that...

ASU is concerned about the retention rate among its students, i.e. percentage of ASU students that return next semester.To do this, ASU randomly selects 200 students and records whether or not they return to ASU the following semester. What is the statistic?

a.	The percentage of the 200 students that returned.
	b.	All ASU students.
	c.	The percentage of all ASU students that returned.
	d.	The 200 ASU students that were selected.

Expert Solution

The correct option is Option a.

Here the population of interest is the collection of all the ASU students.

From this population 200 students have been randomly selected. So the collection of these 200 selected students form the random sample.

Now statistic is any function of sample observations only. Value of a statistic can be completely known once we have the random sample observations.

Now,

Option a. Clearly the percentage of 200 students who returned is equal to (number of students out of these 200 selected students who returned)/200*100 % and this value can be observed if the sample is observed completely. So this is a function of random sample observations only. Hence this is a statistic.

Option b. All ASU students are not in the random sample of 200 students. So clearly this value is a count of total students and its value is no way related to the random sample. So this is not a statistic.

Option c. We have a sample of 200 students and we observe how many of these 200 students returned. The sample observations tell nothing about the value of the percentage of all ASU students that returned and hence it is not a statistic. Moreover this is an unknown population parameter, whose value we want to know.

Option d. The selected 200 ASU students form the random sample. This is a set and not any kind of function of sample observations. Hence it is not a statistic.

So option a is the only correct option.

Hope the solution helps. Thank you.

(If you need further assistance please ask in the comment section)

orchestra answered 2 years ago

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