Question

# What are the breakfast-eating habits of college students? A group of 460 college students was surveyed...

What are the breakfast-eating habits of college students? A group of 460 college students was surveyed over several typical weekdays, and 322 of them reported that they had eaten breakfast that day. Let B be the event of interest—that a college student eats breakfast.

a) Based on this information, what is the estimate of P(B), the probability that a randomly chosen college student eats breakfast?

b) Which of the following would provide even more convincing evidence that, indeed, P(B) is roughly what you estimated above? Check one and explain your choice:

• Out of 10 randomly chosen college students, 7 reported that they had eaten breakfast that day.

• Out of 20 randomly chosen college students, 14 reported that they had eaten breakfast that day.

• Out of 1,000 randomly chosen college students, 700 reported that they had eaten breakfast that day.

Explanation:

a.

P(B) = (no. of students that reported they had breakfast)/(total students surveyed)

= 322/460

= 0.7

b.

answer : the most convincing :

Out of 1,000 randomly chosen college students, 700 reported that they had eaten breakfast that day.

Explanation :

proprtions(p) : 7/10 = 14/20 = 700/1000 = 0.7 = P(B)

the proportion is same for all samples

variance = p*(1-p)/n = 0.7*(1-0.7)/n = 0.21/n

The higher the sample size the more convincing it will be as the variance will be lower so the sample with 1000 college students in which 700 reported that they had eaten breakfast that day is the most convincing

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