Question

1. a sample of college freshmen is surveyed and asked the following question: “what aspect of college were you least prepared for?” all students in the sample answered this question, and the students were able to choose one of the following five options as their answer: academics, financial issues, social issues, life balance, and other. the percentages who chose each option are shown in the table below. if a college administrator decides to consider anyone who selected either social issues or life balance to fall within the category of “personal adjustment,” and if it turns out that 1,260 students in the sample fall into this category of “personal adjustment,” which of the following must have been the total sample size for this survey?

aspect of college	percentage
financial issues	14%
social issues	19%
life balance	17%
other	1%

a. 3,600
b. 3,500
c. 3,450
d. 3,400
e. it’s impossible to answer this question without more information.

Explanation:

Step1: Calculate percentage of "Personal Adjustment"

The percentage of students in the "Personal Adjustment" category is the sum of the percentages of those who chose Social Issues and Life - Balance. So, $19\%+17\% = 36\%$.

Step2: Set up proportion to find sample size

Let the total sample size be $x$. We know that 36% of $x$ is 1260. The proportion is $\frac{36}{100}x=1260$.

Step3: Solve for $x$

We can rewrite the equation as $x=\frac{1260\times100}{36}$. Simplifying, $x = 3500$.

Answer:

B. 3,500