Suppose some students in another class received the following distribution of grades: 30% of the students got an A (4 points); 40% got a B (3); 20% got a C (2); and 10% got a D(1).

(i) Calculate the average grade given out to the students who took this class.

f a sample of size n = 2 is taken from these students, the following sampling distribution results:

[u = xP(x)]

sample: probability: x p

two A's 9%

one A, one B 24%

one A, one C 12%

one A, one D 6%

two B's 16%

one B, one C 16%

one B, one D 8%

two C's 4%

one C, one D 4%

two D's 1%

(ii) Calculate the mean grade () for each sample. (Show above in column under "").

(iii) Calculate the mean of the sample means. [ux = x P(x)]

(iv) Calculate the proportion of B's (p^) in each sample. (Show above in column under "").

(v) Calculate the mean of the sample proportions. [up = p P(p)]

(vi) Answer the following questions by selecting the best word or words from the choices given in bold.

1. The mean of the sample means (ux ) is equal to / less than / greater than the average grade of the students who took the class.

2. The mean of the sample proportions (up ) is equal to / less than / greater than the proportion of students who got a B in the class.

3. The answers to questions 1 and 2 means that x and p are biased / unbiased / binomial estimators.