2. Your statistics lecturer decides to select a random sample of 226 EBCS 1514 students to complete a questionnaire. The number of students in each of the 6 lecturer’s classes is given in the table below. If a proportional random sample is drawn from each class, what is the sample size for each lecturer?

Question

Lecturer
1
2
3
4
5
6
Number of students
420
380
240
480
490
250

Answer 1

To calculate the sample size for each lecturer, we first need to calculate the total number of students in all the classes:

Total number of students = 420 + 380 + 240 + 480 + 490 + 250 = 2260

Now, we can calculate the proportion of students in each lecturer's class relative to the total number of students:

Proportion for lecturer 1: 420/2260 = 0.1858
Proportion for lecturer 2: 380/2260 = 0.1681
Proportion for lecturer 3: 240/2260 = 0.1062
Proportion for lecturer 4: 480/2260 = 0.2124
Proportion for lecturer 5: 490/2260 = 0.2164
Proportion for lecturer 6: 250/2260 = 0.1106

Now, we multiply each proportion by the total sample size of 226 to determine the sample size for each lecturer:

Sample size for lecturer 1: 0.1858 * 226 = 42.02 ≈ 42
Sample size for lecturer 2: 0.1681 * 226 = 37.99 ≈ 38
Sample size for lecturer 3: 0.1062 * 226 = 23.90 ≈ 24
Sample size for lecturer 4: 0.2124 * 226 = 48.05 ≈ 48
Sample size for lecturer 5: 0.2164 * 226 = 48.97 ≈ 49
Sample size for lecturer 6: 0.1106 * 226 = 25.01 ≈ 25

Therefore, the sample size for each lecturer is 42, 38, 24, 48, 49, and 25 respectively.