In each of the scenarios below identify what is wrong and ex

In each of the scenarios below, identify what is wrong and explain why. 1. The provost of a university with 30,000 undergraduate students and 10,000 graduate students wants to conduct a survey of student opinion concerning health care benefits for domestic partners of students. She wants to give every student in the university to have an equal chance of being selected in the survey so she asks the institutional researchers to take a simple random sample of 400 students to conduct the survey. The researcher selects 300 of 30,000 undergraduate students at random (which gives each of them a chance of 300/30,000 = 0.1 to be selected) and 100 of 10,000 graduate students at random (with a chance of 100/10,000 = 0.1 for each). The 400 students chosen make up the sample.

Solution

the thing that is wrong here is the probability of students being selected in the survey.

in the question it is mentioned that out of 30,000 under graduate students 300 students are selected at random and that gives each of them a chance of 300/30,000 = 0.1 to be selected.

but 300/30,000=0.01

so the correct probability of getting selected in the survey of undergraduate students is 0.01 not 0.1

similarly for graduate students also 100/10,000=0.01 not 0.1

so selecting 300 students from 30,000 undergraduate students gives each of them a chance of 0.01 of being selected in the sample. also selecting 100 students from 10,000 graduate students gives each of them a chance of 0.01 of being selected in the sample.

these 400 students chosen make up the sample.