Question

A survey on coffee consumption was conducted among a random sample of students at a university. The results are shown in the table above. Which of the following statements about the students surveyed is NOT supported by the table?

Cups of coffee (per day)

Student Year| 0| 1| 2 or more| Total
Freshman| 25| 9| 16| 50
Sophomore| 5| 19| 26| 50
Junior| 10| 6| 50| 66
Senior| 0| 2| 32| 34
Total| 40| 36| 124| 200

A. A higher percentage of juniors than sophomores drink 2 or more cups of coffee per day.
B. A higher percentage of juniors than seniors drink 2 or more cups of coffee per day.
C. 20% of all students surveyed do not drink coffee.
D. 50% of freshmen do not drink coffee.

Answer 1

In order to find the wrong statements from the options, we will evaluate each option. Let us find the percentage of juniors drinking 2 or more coffee. This is done by dividing the number of junior students that consume 2 or more drinks by the total number of students and multiplying by 100. Hence, Percentage of junior students that consumes 2 or more drinks =75.75%. Similarly, the percentage of sophomore drinking 2 or more coffee $=52\%$ . Percentage of seniors drinking 2 or more coffee $=94.11\%$ . Percentage of students who do not drink coffee $=20\%$ . Percentage of freshmen who do not drink coffee $=50\%$ . Now, evaluate each option.

Complete step-by-step answer:
We have to find the wrong statements from the options which are based on the survey on coffee consumption among a random sample of students at a university.
Let us find the percentage of juniors drinking 2 or more coffee. This is done by dividing the number of junior students that consume 2 or more drinks by the total number of students and multiplying by 100. We can write it as
Percentage of junior students that consumes 2 or more drink $=\dfrac{50}{66}\times 100\%$
Let us simplify this. We will get
Percentage of junior students that consumes 2 or more drink $=\dfrac{5000}{66}\%=75.75\%$
Let us find the percentage of sophomores drinking 2 or more coffee.
Percentage of sophomore drinking 2 or more coffee $=\dfrac{26}{50}\times 100\%=26\times 2\%=52\%$
Now, we can find the percentage of seniors drinking 2 or more coffee. That is
Percentage of seniors drinking 2 or more coffee $=\dfrac{32}{34}\times 100\%=\dfrac{3200}{34}\%=94.11\%$
Let’s find the percentage of students who do not drink coffee. This is shown below
Percentage of students who do not drink coffee $=\dfrac{40}{200}\times 100\%=\dfrac{40}{2}\%=20\%$
Now, we can find the percentage of freshmen who do not drink coffee.
Percentage of freshman who do not drink coffee $=\dfrac{25}{50}\times 100\%=25\times 2\%=50\%$
Let us observe the options.
Option A says that a higher percentage of juniors than sophomores drink 2 or more cups of coffee per day. We found that the percentage of junior students that consumes 2 or more drinks =75.75% that is greater than the percentage of sophomore drinking 2 or more coffee (52%). Hence, option A is correct.
Now, we can consider option B. Percentage of junior students that consumes 2 or more drinks is 75.75% while that of seniors is 94.11%. Seniors consume 2 or more coffee than junior. Hence, option B is incorrect.
Let us move to option C. We found that 20% of all students surveyed do not drink coffee. Hence, option C is correct.
Now, let’s evaluate option D. We found that 50% of freshmen do not drink coffee. Hence, option D is correct.

So, the correct answer is “Option B”.

Note: Don't forget to multiply by 100 to find the percentage. Do not find the required percentage by dividing the total number of students by the number of students, say junior students, and multiplying by 100. Some students might just look at the values in the table and try to conclude their answer without finding the percentages, but this is not valid since the total number of students for each category is different.