The following table represents the test scores, scaled between o and 6, of six s

Question

The following table represents the test scores, scaled between o and 6, of six students and their responses to the question "Do you like the cafeteria food?" (a) what is the mean score of six students? (b) What is the proportion of Yes' of six students? (c) How many different samples of size 3 can be chosen? (d) List all different possible samples of 3 students. (e) Compute the mean score and the proportion of "res' for each sample. (f) Compute the mean of mean scores of all samples. (g) Compute the mean of proportions of all samples. Here is an example with five. Let's say we have five students. (a) Mean score of five students (2+ 2+ 3+ 4 +5)/5= 6.4 (b) Proportion of 'Yes' of five students 3/5= 0.6 (c) There are s_C_3=10 many different samples of size 3. (d) - (e) Compute the mean of all sample means = 2.33+ 2.67 +3 +3+ 3.33+ 3.67 +3 +3.33 +3.67 + 4/10 = 6.4 (g) Compute the mean of all sample proportions = 0.67+ 0.33 +0.67+ 0.33+ 0.67+ 0.33 +0.67 +1 +0.67+ 0.67/10 = 0.6

Explanation / Answer

Solution:

a. Mean score of six students = (2 + 2 + 3 + 4 + 5 + 7)/6 = 23/6 = 3.833

b. Proportion of yes of six students = 4/6 = 66.67%

c. There are 6C3 =20 many different samples of size 3.

d. - e.

f. Mean of mean scores of all samples = (2.33 + 2.67+3 + 3.67 + 3 + 3.33 + 4 + 3.67 + 4.33 +4.67 + 3 + 3.33 + 4 + 3.67 + 4.33 + 4.67 + 4 + 4.67 + 5 + 5.33)/20 = 3.83

g. Mean of all sample proportions = (0.67 + 0.33 + 0.33 + 0.33 + 0.33 + 0.33 + 0.67 + 0.33 + 0.33 + 0.67 + 0.67 + 0.67 + 1 + 0.67 + 0.67 + 1 + 0.67 + 0.67 + 1 + 0.67 + 0.67 + 1 + 0.67)/20 = 0.60

Sample Individuals Mean Proportion of "yes" 1 A, B, C 2.33 0.67 2 A, B, D 2.67 0.33 3 A, B, E 9 0.33 4 A, B, F 3.67 0.33 5 A, C, D 3 0.33 6 A, C, E 3.33 0.33 7 A, C, F 4 0.67 8 A, D, E 3.67 0.33 9 A, D, F 4.33 0.33 10 A, E, F 4.67 0.67 11 B, C, D 3 0.67 12 B, C, E 3.33 0.67 13 B, C, F 4 1.00 14 B, D, E 3.67 0.67 15 B, D, F 4.33 0.67 16 B, E, F 4.67 1.00 17 C, D, E 4 0.67 18 C, D, F 4.67 0.67 19 C, E, F 5 1.00 20 D, E, F 5.33 0.67

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