Question

(Two-Way Frequency Tables MC)

Some researchers claim there is an association between taking vitamins and gaining weight. They took a random sample of people living in Boston, Massachusetts, and recorded whether they took vitamins and whether they gained weight. The results are shown in the following two-way table:


Has Gained Weight Has Not Gained Weight Row Totals
Does not take vitamins 16.9% 6.2% 23.1%
Takes one vitamin per day 11.4% 16% 27.4%
Takes more than one vitamin per day 23.5% 26% 49.5%
Column Totals 51.8% 48.2% 1


A student reading the results stated that more than half of the study participants are taking vitamins. Determine if the student is correct.
Yes, because 23.5% take one vitamin and 48.2% take more than one vitamin, which is a total of 71.7% taking vitamins.
Yes, because 27.4% take one vitamin and 49.5% take more than one vitamin, which is a total of 76.9% taking vitamins.
No, because 11.4% take one vitamin and 23.5% take more than one vitamin, which is a total of 34.9% taking vitamins.
No, because 16% take one vitamin and 26% take more than one vitamin, which is a total of 42% taking vitamins.

Answer 1

After adding the row totals for those taking one vitamin per day (27.4%) and more than one vitamin per day (49.5%), it is clear that 76.9% of the study participants are taking vitamins, so the statement is correct.

Step-by-step explanation:

To determine if the statement that more than half of the study participants are taking vitamins is correct, we must look at the row totals for those who take one vitamin per day and those who take more than one vitamin per day. The row total for participants that take one vitamin per day is 27.4%. The row total for those who take more than one vitamin per day is 49.5%. To find the total percentage of participants taking vitamins, we add these two percentages together:

27.4% + 49.5% = 76.9%

Therefore, more than half of the participants in the study are taking vitamins. The correct answer is: Yes, because 27.4% take one vitamin and 49.5% take more than one vitamin, which is a total of 76.9% taking vitamins.

Answer 2

B. Yes, because 27.4% take one vitamin and 49.5% take more than one vitamin, which is a total of 76.9% taking vitamins.

Step-by-step explanation:

You must add the percentages of the subjects and took vitamins AND did NOT gain weight. The other answer only adds the percentages of those who took vitamins and gained weight. You're looking for the percentage of everyone who took vitamins, regardless of if they gained weight or not.

11.4% + 16% = 27.4% - Takes one vitamin per day
23.5% + 26% = 49.5% - Takes more than one vitamin per day

27.4% + 49.5% = 76.9%

Therefore the student is correct, since it is more than 50% of the participants.