A Math 243 class has 24 students. Suppose the class has 4 male Sophomores and 7

Question

A Math 243 class has 24 students. Suppose the class has 4 male Sophomores and 7 male Juniors, and

has 5 female Sophomores and 8 female Juniors. What is the marginal distribution of gender in the

class?

2. In the example in (1), what is the conditional distribution of gender among Sophomores in the class?

3. Using the example from (1), which is more helpful for finding a relationship between gender and year

in school: marginal distributions of gender and year, or conditional distributions of gender, given year?

4. In your own words, explain Simpson’s Paradox.

Explanation / Answer

following information has been generated from the given data

(1) marginal distribution of gender

(2) conditinal distribution of

(3) conditional distribution is more helpful look the relationship between gender and year.

A conditional distribution is a probability distribution for a sub-population. In other words, it shows the probability that a randomly selected item in a sub-population has a characteristic you’re interested in.

(4)The Paradox is named after the statistician who discovered something unusual in the 1960s. It’s a great example of how stats can be wrong. The paradox is that averages can be silly and misleading. Sometimes they can be just plain baffling. it is like a phenomenon in probability and statistics, in which a trend appears in different groups of data but disappears or reverses when these groups are combined. It is sometimes given the descriptive title reversal paradox or amalgamation paradox. Suppose the English department admits quite a high proportion of applicants, while the maths department is more choosy and admits only a small proportion. Now suppose that most of the male applicants apply to the English department. Then this drives up the overall percentage of successful male applicants, as English is easier to get into. Similarly, if most women apply to the maths department, then this lowers the overall percentage of successful women applicants, because maths is harder to get into. So it can happen that, although neither department discriminates against women, the overall percentage of successful female applicants is lower than that for males.

frequency sophomores juniors total male 4 7 11 gender felmale 5 8 13 total 9 15 24 proprotion/probability sophomores juniors total male 1/6 7/24 11/24 gender felmale 5/24 1/3 13/24 total 3/8 5/8 1     

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