A school principal wants to know the average number of extracurricular activity students in her school are involved in she assigned each student a number from one to 100 to 415 using a random number generator she selected 200 students to be part of the sample she conducted the students she concluded that the students are involved in an average of two extracurricular activities is the principles conclusion valid

Question

A school principal wants to know the average number of extracurricular activity students in her school are involved in she assigned each student a number from one to 100 to 415 using a random number generator she selected 200 students to be part of the sample she conducted the students she concluded that the students are involved in an average of two extracurricular activities is the principles conclusion valid

Answer 1

To determine if the principal's conclusion is valid, we need to calculate the average number of extracurricular activities of the 200 students in the sample.

Let's say the number of extracurricular activities each student is involved in is represented by the variable x.

Since each student was assigned a number from 1 to 100, the total number of extracurricular activities across all 415 students can be calculated as:
Total activities = 1 + 2 + 3 + ... + 100 = 100 * 101 / 2 = 5050

The average number of extracurricular activities for the entire school is:
Average activities = Total activities / Total students = 5050 / 415 ≈ 12.16

Therefore, the average number of extracurricular activities for the entire school is approximately 12.16, not 2 as concluded by the principal. This indicates that the principle's conclusion is not valid.