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