Question

I want to find out what the undergraduate student body thinks about the school proposal to reallocate funds marked for academic development (hiring more faculty/adding more classes) towards the expansion of the Campus Gym. So I head over to Campus Gym and set up a booth next to the entrance of the building. I ask everyone who passes by whether or not they support the proposal, and get 500 responses.

1. Will my sampling scheme lead to sampling bias? Will it lead to sampling variability? Explain.  
2. Do you think that the sample statistics from this study will closely approximate the population parameters? If not, use two or more terms that we have learned in this course to tell me what is wrong with my sampling scheme. (These terms should not include “sampling bias” or “sampling variability.”)

Answer 1

1. It is reasonable to assume that not all the undergraduate student body members prefer to go to the gym.As I have sampled only those people who have come to the gym there is obviously a sampling bias.As we have not taken the sample from all parts of the population and it is reasonable to assume the proportion of people who come to the gym and want findings to be spent on gym is likely to larger than that proportion of people who do not go to the gym. In this case sampling variability will be less than it should be in an sample that represents the whole population.Because here we are sampling only those kind of people who go to the gym and exclude the people who do not go to the gym.so our sample lack variation among units.
2. As discussed in earlier section chosing such kind of sample will lead to sampling bias.so sample statistic formed from such kind of sample can no way be a good estimate of population parameters.Besides that here the sampling scheme is non probabilistic in nature as the students who do not go to the gym have 0 probability of being included in the sample.Here if we divide our population in 2 groups those who go to gym and those who do not and assume these 2 groups of people are homogenous within the group.(which is quite reasonable) then the sampling scheme we should have employed here is stratified random sampling which we have not so it can lead to a good estimate of population parameters