Consider the following situation: A local college advertises that 75% of its stu
ID: 3226633 • Letter: C
Question
Consider the following situation:
A local college advertises that 75% of its students find jobs in their field of study within six months of graduation. To test this, an independent researcher recruits 82 random graduates from the past year and finds that 51 found a job in their field within six months. From this data they construct a 95% confidence interval for the actual proportion of students who find a job in their field of study within six months and it is (0.52 , 0.73).
Use what you know about confidence intervals and now rare/unusual events to make a statement about the validity of the claim made by the local college.
Explanation / Answer
Answer
Given that 95% confidence interval for the actual proportion of students who find a job in their field of study within six months is (0.52 , 0.73)
That is, with 95% confidence we can claim that the actual proportion of students who find a job in their field of study within six months is within (52%, 73%).
The local college claims that 75% of its students find jobs in their field of study within six months of graduation. Since the 95% confidence interval does not include 75%, we can reject the claim with 95% confidence. In fact, 75% success rate is an unusual event as it is outside the 95% confidence interval.
Thus with 95% confidence, we can reject the claim of the local college.