A survey given to a random sample of 250 students at a small University asks which facility they use most often. The results are shown in the table above. If the results of the sample are projected to the entire student population 1,000 students, which of the following is the difference in the number of students who most often use the Union compared to the students who most often use the Music Hall? Recreation Center Library Union Music Hall 60 80 70 40

Question

A survey given to a random sample of 250 students at a small University asks which facility they use most often. The results are shown in the table above. If the results of the sample are projected to the entire student population 1,000 students, which of the following is the difference in the number of students who most often use the Union compared to the students who most often use the Music Hall? Recreation Center Library Union Music Hall 60 80 70 40

A.120***

B. 280

C. 160

D. 300

Answer 1

looks good

Answer 2

To find the difference in the number of students who most often use the Union compared to the students who most often use the Music Hall, we need to calculate the projected number of students using each facility based on the survey results.

First, let's calculate the proportion of students in the sample who use each facility most often:

Union: 70/250 = 0.28
Music Hall: 40/250 = 0.16

Next, let's project these proportions to the entire student population of 1,000 students:

Union: 0.28 * 1000 = 280
Music Hall: 0.16 * 1000 = 160

Finally, we can find the difference between the projected number of students using the Union and the projected number of students using the Music Hall:

280 - 160 = 120

Therefore, the difference in the number of students who most often use the Union compared to the students who most often use the Music Hall is 120.

So, the answer is A. 120.

Answer 3

To find the difference in the number of students who most often use the Union compared to the students who most often use the Music Hall, we need to calculate the projected number of students for each facility based on the given sample.

First, we find the percentage of students who most often use each facility in the sample:

- Union: 70 out of 250 students (70/250) = 28% of the sample
- Music Hall: 40 out of 250 students (40/250) = 16% of the sample

Next, we project these percentages to the entire student population of 1,000 students:

- Union: 28% of 1,000 students = 0.28 * 1,000 = 280 students
- Music Hall: 16% of 1,000 students = 0.16 * 1,000 = 160 students

Finally, to find the difference, we subtract the number of students who most often use the Music Hall from the number of students who most often use the Union:

- Difference = 280 - 160 = 120

Therefore, the correct answer is A. 120.