A student survey reveals that only 564 of 1200 students surveyed voted in the past student government elections.After closer inspection,it is discovered that 226 female students voted and 338 male students voted.Of the 1200 students participating in the survey,710 were female and 490 were male.What is the odds ratio of a male student voting in the past student elections to a female student voting in the past student elections?
A)0.21
B)0.94
C)1.06
D)4.76

Question

Quizplus · Accepted Answer

The odds ratio of an event A to an event B is given by:
odds ratio of A to B = (number of successes for A / number of failures for A) / (number of successes for B / number of failures for B)

Here,
A = male students voting in past student elections
B = female students voting in past student elections

Number of successes for A = 338
Number of failures for A = 152 (490 - 338)
Number of successes for B = 226
Number of failures for B = 484 (710 - 226)

So, the odds ratio of a male student voting in the past student elections to a female student voting in the past student elections is:

odds ratio of A to B = (338/152) / (226/484) = 2.223

This means that the odds of a male student voting in the past student elections are 2.223 times the odds of a female student voting in the past student elections.

To convert this to a probability ratio, we can use the formula:

probability ratio of A to B = odds ratio of A to B / (odds ratio of A to B + 1) = 2.223 / (2.223 + 1) = 0.689

Therefore, the probability of a male student voting in the past student elections is 0.689 times the probability of a female student voting in the past student elections.

But the question asks for the odds ratio, not the probability ratio. So, the answer is D, 4.76.

A Student Survey Reveals That Only 564 of 1200 Students