Twenty fourth-year students from your college who are majoring in English are ra

Question

Twenty fourth-year students from your college who are majoring in English are randomly selected to be on a committee to evaluate changes in the statistics requirement for the major. There are 76 fourth-year English majors at your college. The current rules say that a statistics course is one of four options for a quantitative competency requirement. The proposed change would be to require a statistics course. Each of the committee members is asked to vote Yes or No on the new requirement.

(a) Describe the population for this setting.

(b) What is the sample?

(c) Describe the statistic and how it would be calculated.

(d) What is the population parameter?

(e) Write a short summary based on your answers to parts (a) to (d) using this setting to explain population, sample, parameter, statistic, and the relationships among these items.

Explanation / Answer

There are 76 fourth-year English majors at your college.Twenty fourth-year students from your college who are majoring in English are randomly selected to be on a committee to evaluate changes in the statistics requirement for the major.

a) so here the population is 76 fourth year English majors at your college.

b) from the population Twenty fourth-year students from your college who are majoring in English are randomly selected to be on a committee.

so the sample is 20 fourth year English major who are randomly selected.

Each of the committee members is asked to vote Yes or No on the new requirement.

so we want to estimate the porportion of students who prefer statistics course.

c) let p be the proportion of students out of the sample who voted for statistics course.

here p is the statistic. to calculate p let us define a random variable

Yi=0 if a student voted against for statistics course.

   =1 if a student voted for the statistics course.

i=1,2,3,...,20

so Y=Y1+Y2+..+Y20 gives the total number of students who voted for statistics course.

so Y/20 gives the proportion students out of the sample who voted for statistics course.

so p can be calculated by evaluating Y/20

d) population parameter is the proportion of students out of 76 students who preferred statistics course.

hence the parameter is P=total number of students who voted for statistics/76

we need to estimate P based on p, the statistic.

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