Question

At a university, 12% of students smoke. Calculate the expected number of smokers in a random sample of 140 students from this university (please do not round your answer): The university gym opens at 9 am on Saturday mornings. One Saturday morning at 8:55 am there are 24 students outside the gym waiting for it to open. Should you use the same approach from part (a) to calculate the expected number of smokers among these 24 students? No, it is unlikely that smoking habits and waking up early to go to the gym on Saturday are independent Yes, it is reasonable to believe that people who go to the gym when it first opens on Saturday mornings is a representative sample

Answer 1

Answer:

a) The expected number of smokers in a random sample of 140 students from this university is 16.8 smokers.

b) No, it is unlikely that smoking habits and waking up early to go to the gym on Saturday are independent.

Step-by-step explanation:

To calculate the expected numbers of smokers in a sample with size n=140 and proportion p=12%, we use the expected value of the binomial distribution:

$E(x)=n\cdot p=140\cdot 0.12=16.8$

The expected number of smokers in a random sample of 140 students from this university is 16.8 smokers.

If we take a sample at the opening of the gym, the sample is not expected to be representative of the population of the students. Most of the students that go to the gym usually have healthy habits, so the proportions of smokers is expected to be lower than the average of the university population.