A simple random sample of 50 students is taken from a class of 300 students. In the class,

* the average midterm score is 67 and the SD is 12

* there are 72 women

Let W be the number of women in the sample, and let S be the average midterm score of the sampled students.

1 - Find E(W)
2 - Find SE(W)
3 - Find E(S)
4 - Find SE(S)

Find E(W) is 12, but I don't know the others. Could someone help me?

E(S)=11,1667

This E(S) is wrong

E(S) = 67

To find the answers to the questions, we need to use the formulas for expected value (E) and standard error (SE) and apply them to the given information. Let's go step by step:

1 - Find E(W):
Expected value (E) is the average or mean value that we would expect over many repeated experiments. For a simple random sample, the expected value of a variable can be found by multiplying its probability of occurrence by the value of the variable. In this case, E(W) represents the expected number of women in the sample.

Given that there are 72 women in a class of 300 students, the probability of selecting a woman in the sample is calculated as 72/300. Therefore, to find E(W), we multiply this probability by the total sample size:

E(W) = (72/300) * 50
E(W) = 12

So, the expected number of women in the sample (E(W)) is 12.

2 - Find SE(W):
The standard error (SE) measures the variability or uncertainty around the expected value of a random variable. For a simple random sample, the standard error of a proportion can be calculated using the formula:

SE(W) = sqrt[(p * (1-p)) / n]

Where p represents the probability of success in each trial (in this case, the probability of selecting a woman) and n is the sample size.

Using the given information, the probability of selecting a woman (p) is 72/300, and the sample size (n) is 50. Plugging these values into the formula, we can calculate SE(W):

SE(W) = sqrt[(72/300) * (1 - 72/300) / 50]
SE(W) ≈ 0.057

So, the standard error of the number of women in the sample (SE(W)) is approximately 0.057.

3 - Find E(S):
Similarly, we can find the expected value of the average midterm score (E(S)) by multiplying the probability of selecting a student by the average score:

E(S) = (67 * 50) / 300
E(S) ≈ 11.17

So, the expected average midterm score (E(S)) of the sampled students is approximately 11.17.

4 - Find SE(S):
To calculate the standard error of the average midterm score (SE(S)), we need to use the standard deviation (SD) of the population and the sample size (n). The standard error of the mean can be calculated using the formula:

SE(S) = SD / sqrt(n)

Given that the population standard deviation (SD) is 12 and the sample size (n) is 50, we can plug these values into the formula to find SE(S):

SE(S) = 12 / sqrt(50)
SE(S) ≈ 1.697

So, the standard error of the average midterm score (SE(S)) is approximately 1.697.