Question

Suppose the proportion of all college students who have changed their major in the last two semesters is 60%. If a class of 200 students is considered what is the probability that the proportion of students who may change their major in the next 2 semesters is at least 56%?

Answer 1

ANSWER:

P hat = 0.56

p = 0.60

q = 1 - p = 1 - 0.60 = 0.40

n = 200

proportion of students who may change their major in last 2 semesters is at least 56% = p hat - p / (pq / n) ^ 1 / 2

proportion of students who may change their major in last 2 semesters is at least 56% = 0.56 - 0.6 / (0.6 * 0.4 / 200) ^ 1 / 2

proportion of students who may change their major in last 2 semesters is at least 56% = 0.04 / (0.0012) ^ 1 / 2

proportion of students who may change their major in last 2 semesters is at least 56% = 0.04 / 0.034641

proportion of students who may change their major in last 2 semesters is at least 56% = 1.1547

looking inthe z table we get that the value of 1.1547 is 0.8749

so the proportion of students who may changed their major in last 2 semesters is 0.8749