Question

a survey was conducted to find out whether students prefer studying in a quiet environment or with music at different times of the day. the results are shown in the two - way table below:
based on the data, which of the following statements is true?
students are more likely to prefer a quiet environment at night.
more students prefer a quiet environment overall.
more students prefer studying with music at night than in the afternoon.

Explanation:

Step1: Calculate the proportion of students who prefer quiet environment at night

The number of students who prefer quiet environment at night is \(20\), and the total number of students who study at night is \(60\). The proportion is \(\frac{20}{60}=\frac{1}{3}\approx0.33\)

Step2: Calculate the proportion of students who prefer quiet environment in the afternoon

The number of students who prefer quiet environment in the afternoon is \(25\), and the total number of students who study in the afternoon is \(40\). The proportion is \(\frac{25}{40} = 0.625\)

Step3: Calculate the proportion of students who prefer quiet environment overall

The number of students who prefer quiet environment overall is \(45\), and the total number of students is \(100\). The proportion is \(\frac{45}{100}=0.45\)

Step4: Calculate the proportion of students who prefer music at night

The number of students who prefer music at night is \(40\), and the total number of students who study at night is \(60\). The proportion is \(\frac{40}{60}=\frac{2}{3}\approx0.67\)

Step5: Calculate the proportion of students who prefer music in the afternoon

The number of students who prefer music in the afternoon is \(15\), and the total number of students who study in the afternoon is \(40\). The proportion is \(\frac{15}{40}=0.375\)

Answer:

Students are more likely to prefer a quiet environment overall.