Given that the Number of Grantees of a Driver's License in a small country in the month of April are ....
1,200 for professionsl
3,350 for non-professional
2,450 for students
If you want to make a study of the correlation between driving habits and number of vehicular accidents that these new drivers met after securing a license, how many of them will you study if your sample size is 600 using a "Simple Stratified Random Sampling?"
To determine the number of grantees you should study using a simple stratified random sampling technique, you need to first calculate the proportion of each stratum in relation to the total population.
1. Find the total number of grantees:
Total grantees = Professional grantees + Non-professional grantees + Student grantees
Total grantees = 1,200 + 3,350 + 2,450 = 7,000
2. Calculate the proportion of each stratum:
Proportion of professional grantees = Professional grantees / Total grantees
Proportion of professional grantees = 1,200 / 7,000 = 0.1714 or 17.14%
Proportion of non-professional grantees = Non-professional grantees / Total grantees
Proportion of non-professional grantees = 3,350 / 7,000 = 0.4786 or 47.86%
Proportion of student grantees = Student grantees / Total grantees
Proportion of student grantees = 2,450 / 7,000 = 0.3500 or 35.00%
3. Determine the sample size for each stratum:
Sample size for professional grantees = Proportion of professional grantees * Sample size
Sample size for professional grantees = 0.1714 * 600 = 102.84 or approximately 103
Sample size for non-professional grantees = Proportion of non-professional grantees * Sample size
Sample size for non-professional grantees = 0.4786 * 600 = 287.16 or approximately 287
Sample size for student grantees = Proportion of student grantees * Sample size
Sample size for student grantees = 0.3500 * 600 = 210.00 or 210
4. Sum up the sample sizes to determine the total number of grantees you will study:
Total sample size = Sample size for professional grantees + Sample size for non-professional grantees + Sample size for student grantees
Total sample size = 103 + 287 + 210 = 600
Therefore, you will study 600 grantees if you use simple stratified random sampling, which is the same size as your desired sample size.