Question

It has been reported that 5% of all undergraduate students in the U.S. who take an introductory statistics course will continue their education in statistics. A researcher believes that this value is too low for the recent undergraduate students who have taken an introductory statistics course at his university, California University. A listing of all undergraduate students at California University who did take an introductory statistics course sometime over the past 4 years was generated and a random sample of 400 students from this list was selected. Of the 400 undergraduate students, 80 (or 20%) did continue their education in statistics.
1. In this study, the population of interest is:_______

a. All undergraduate students in the U.S. who took an introductory statistics course.
b. All recent undergraduate students who took an introductory statistics course at California University over the past 4 years.
c. The 400 undergraduate students at California University who took an introductory statiistics course over the past 4 years.
d. The 80 undergraduate students at California University who took an introductory statiistics course over the past 4 years and who did continue their education in statistics.

2. In this study, the 5% value could be considered a:______

a. a statistic, because it is a numerical summary for a sample.
b. a statistic, because it is a numerical summary for a population.
c. a parameter, because it is a numerical summary for a sample.
d. a parameter, because it is a numerical summary for a population.

3. In this study, the 20% value can be considered a:________

a. a statistic, because it is a numerical summary for a sample.
b. a statistic, because it is a numerical summary for a population.
c. a parameter, because it is a numerical summary for a sample.
d. a parameter, because it is a numerical summary for a population.

Answer 1

Answer:

(1) All undergraduate students in the U.S. who took an introductory statistics course.

(2) a parameter, because it is a numerical summary for a population.

(3) a statistic, because it is a numerical summary for a sample.

Step-by-step explanation:

We are given that it has been reported that 5% of all undergraduate students in the U.S. who take an introductory statistics course will continue their education in statistics.

A random sample of 400 students from this list was selected. Of the 400 undergraduate students, 80 (or 20%) did continue their education in statistics.

(1) In this study, the population of interest is;

All undergraduate students in the U.S. who took an introductory statistics course because the researcher believes that the value which has been reported is too low for the recent undergraduate students who have taken an introductory statistics course at his university.

(2) In this study, the 5% value could be considered a parameter, because it is a numerical summary for a population which states that this value represents all undergraduate students in the U.S. who take an introductory statistics course will continue their education in statistics.

(3) In this study, the 20% value can be considered a statistic, because it is a numerical summary for a sample which represents the % of students who did continue their education in statistics out of the 400 selected undergraduate students.