A random sample of 1200 U.S. college students was asked, "What is your perception of your own body? Do you feel that you are overweight, underweight, or about right?" The two-way table summarizes the data on perceived body image by gender. begin{array}{c|c} & Female Male & Total hline About right & 560 295 & 855 hline Overweight & 163 72 & 235 hline Underweight & 37 73 & 110 hline Total & 760 440 & 1200 end{array} What proportion of the sample is female?

Question
Two-way tables
asked 2021-02-12
A random sample of 1200 U.S. college students was asked, "What is your perception of your own body? Do you feel that you are overweight, underweight, or about right?" The two-way table summarizes the data on perceived body image by gender.
\(\begin{array}{c|c} & Female\ \ \ \ \ \ Male & Total \\ \hline About\ right & 560\ \ \ \ \ \ \ \ \ \ 295 & 855\\ \hline Overweight & 163\ \ \ \ \ \ \ \ \ \ 72 & 235 \\ \hline Underweight & 37\ \ \ \ \ \ \ \ \ \ \ \ 73 & 110 \\ \hline Total & 760\ \ \ \ \ \ \ \ \ \ 440 & 1200 \end{array}\)
What proportion of the sample is female?

Answers (1)

2021-02-13
The study includes 1200 U.S. college students.
\(\begin{array}{c|c} & Female\ \ \ \ \ \ Male & Total \\ \hline About\ right & 560\ \ \ \ \ \ \ \ \ \ 295 & 855\\ \hline Overweight & 163\ \ \ \ \ \ \ \ \ \ 72 & 235 \\ \hline Underweight & 37\ \ \ \ \ \ \ \ \ \ \ \ 73 & 110 \\ \hline Total & 760\ \ \ \ \ \ \ \ \ \ 440 & 1200 \end{array}\)
We then note that 760 of the 1200 U.S. college students are female (as 760 is mentioned in the row ”Total” and in the column ”Female” of the table). \(\frac{760}{1200}=\frac{19}{30}\approx0.6333=63.33\%\) Thus approximately 0.6333 of the respondents are female. Result 0.6333
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