Question

The following binary data represent the students taking a class where "1" is for students who are business majors and "0" for other majors. 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 If we take repeated samples of size n = 40 from this population of the expected value of sample proportions would be ______.

Answer 1

If we take repeated samples of size n = 40 from this population, the expected value of sample proportions would be approximately 0.75.

Step-by-step explanation:

To calculate the expected value of sample proportions, sum the individual probabilities of success (students who are business majors) for each observation and then divide by the sample size. The sum of "1"s (business majors) in the given data is 60 out of 80 total observations. Therefore, the expected value of sample proportions (P) is calculated as 60/80 = 0.75. This means that if we repeatedly draw samples of size 40 from this population, we can expect the sample proportion of business majors to be around 0.75 on average.