Question

Students are voting on the color of T-shirts to wear on their field trip. There are 160 students-65 boys and 95 girls-going on

the field trip. A random sample of students is chosen. Surveying the random sample produced a representative sample of the
population. Which was most likely true of the representative sample?
The representative sample contained all 160 students.
The representative sample contained more boys than girls.
The representative sample contained more girls than boys.
The representative sample contained an equal number of boys and girls.
Pls answer

Answer 1

The representative sample contained more girls than boys.

Explanation:

Solution:-

- Denote the number of boys going on trip, B = 65

- Denote the number of boys going on trip, G = 95

- The total of T = 160 students are going on the trip.

- We are to randomly select a representative sample from the population of students with T = 160 students in total.

- The proportion of boys population ( p ) among the total population can be determined:

p = B / T

p = 65 / 160

p = 0.40625

- The proportion of girls population ( q ) among the total population can be determined:

q = G / T

q = 95 / 160

q = 0.59375

- For us to select a representative group of sample size ( n ) from the population of 160 student. The possibility of finding a girl on that representative group is q = 59.4 % while the possibility of finding a boy on that representative group is p = 40.6 %.

Answer: We are likely to see more girls as part of the representative group as compared to boys.