MAT 1272 Statistics, SP2014

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    Ezra Halleck

    Circle any of the following which constitute a population (as opposed to a sample).
    a. Incomes for the 532 resident families in a village of New York
    b. Salaries of all full-time employees of a company
    c. Number of absences during the semester for each of the students in a class
    d. Number of cars owned by each of 100 families selected randomly via phone calls
    e. Color of hair of the first 25 girls who pass the entrance doorway to a school cafeteria.



    I circled letters (b) and (c).


    Ezra Halleck

    Your choices for population so far are correct. However, you didn’t catch them all. Remember that a population may be considered as a sample if a larger set is looked at. Perhaps I should have stated the problem as “Circle any of the following which MAY constitute a population”.

    For those who need to get in participation, can you discuss how the samples (not populations) might not be representative?


    Chana Max, RN

    i circled (a) as well since its all the families in the village.


    Ezra Halleck

    Yes cmax you are right, (a) should be circled as well. So (d) and (e) are samples. I repeat my earlier question:
    how might these 2 samples not be representative?


    Caroline Carreño

    a, b, and c should be circled.

    These 2 samples might not be represented to be populations for d) 100 is too small a sample (and 100 families where? … 100 families from around the world? 100 families from Brooklyn? 100 families on a cruise ship?), and e) b/c hair color changes depending on preferences contiguous of time and place (where in the world)… although it may be an interesting thing to do considering when and where these hair color trends are present


    Ezra Halleck

    Those are thoughtful remarks Caroline.
    There are several issues here. The size of an interval and whether it will be big enough to make decisions is a well-understood topic and you have addressed it.
    However, whether a sample is REPRESENTATIVE of the population in question is a huge area of study and difficulty. For example, doing surveys via telephone is problematic. Is it just land-line? If it is cellphone as well, how do you account for the fact that typically each family member has a cell phone. Also, how do you account for the fact that many people do not respond to telephone surveys or screen all their calls?
    As for the hair color example, how do you know that clustering did not happen. Perhaps all the girls of one ethnic group go to the cafeteria together. Perhaps a better way would be to record the color of every 10th girl that came in. If there are 250 girls altogether, you are likely to more representative sample than just the first 25. Or even more sophisticated would be to do a stratified sampling, where you sample among each ethnic group in proportion to their makeup in the population.

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