Terminology
Samples are based on drawing random names/numbers out of a hat or using a computer to generate a random list
What is Random Sampling?
Characteristics taken from all members of the population
Census
A school wants to know how students feel about the new cafeteria menu. They send a survey to 200 students, and 150 students complete the survey.
Find the response rate.
(150/200)*100= 75%
It is a set of elements under consideration for statistical purposes. It could be a group of people or a set of objects.
Population
It's a subset of the population
Sample
A school has 800 students. The school administration wants to find out how many students participate in sports activities outside school hours.
Explain how to choose a simple random sample of 50 students
Put the students' names in a roulette and randomly select 50 of them, or assign each student a number from 1 to 800 and use a random number generator to select 50 different numbers.
Involves organizing the population by a criterion and then selecting a sample at regular intervals rather than by random selection.
What is Systematic Sampling?
It happens when there isn't a fair representation of the population
Bias
A school has 800 students. The school administration wants to find out how many students participate in sports activities outside school hours.
Explain how to choose a systematic sample of 40 students
800/40=20
Organize the students (in alphabetical order or another criterion), select the first student randomly, and then choose every 20 students
A method of sampling that involves separating members of a population into subsets and then choosing a proportional sample from each randomly
What is Stratified Sampling?
It's the process of using data analysis and methods to draw conclusions, make generalizations, or test claims about a larger population based on a smaller sample
Statistical inference
Number of students per grade:
Grade 9 = 320
Grade 10= 280
Grade 11= 200
Total population= 800
Calculate the number of students to be taken from the 9th grade if the sample size is 50 students
(320)/(800) * 50 =20
Formula to calculate the proportion in a group by applying stratified sampling.
(# elements of the group)/(population size)* Sample size
What sampling technique is suitable for the following situation:
A school has 800 students. The school administration wants to find out how many students participate in sports activities outside school hours.
Simple Random Sampling or systematic sampling
Number of students per grade:
Grade 9 = 320
Grade 10= 280
Grade 11= 200
Total population= 800
Calculate the number of students to be taken from the 10th grade if the sample size is 50 students
(280)/(800) * 50 =17.5 ≈ 18