Simple Random Sampling

追加: 2026-05-17

[00:00:00]hi guys welcome back so now that we know that different types of variables and how to classify them and we know how to set up our study if we want to do an observational study or a design experiment now it's time to figure out how to get people in our study and we do that by chance so we use random sampling and the reason we use random sampling is because that is the way we are going to be able to mimic the actual population the most if it's completely random okay so random sampling let's take a look at the definition okay so random sampling is the process of using chance to select individuals from a population to be included in the sample and if we don't use a chance if it's not random then we call it a convenience sample and if convenience is used to get the sample then the results are useless alright so convenience sample is we can think of it as non-random and so convenience samples will be self selecting or voluntary response sample self selecting or voluntary response sample so for example you are listening to the radio and you hear about a topic and you had a very strong opinion about it right and you call in to give you opinion well everybody calling in is giving strong opinions so that's not what's happening in the population Hey and another example of a convenience sample is self-serving sample self-serving sample so for instance if let's say Colgate I wanted to conduct a survey about the best-tasting toothpaste best-tasting toothpaste more like a basic cleansing toothpaste I guess right I would not trust the survey performed by Colgate itself because they're probably going to tilt the survey so they look great in the data likewise some pharmaceutical companies they self test their own drugs kind of the same self serving sample okay so those samples are bad and biased random sampling is good it represents the population better and that's the whole point right we need a random sample so we can make a conclusion about the population so we want our sample to look like the population okay so the types of random sampling that we're going to see in this section is called simple random sampling and s rs4 short okay and in the next section we're going to be looking at three others stratified stratified sampling okay and systematic sampling and finally cluster sampling all valid types of a sampling and we determine which method to use based on the situation some random sampling methods are better in other situations and it will talk more about that in the next section okay so let's take a look at simple random sampling so here is our definition a sample of a size end little end we have some notation that we're going to be using for the rest of this semester this guy right here and so little n is the size of a sample so n is size of a sample okay and the big end is a population size so that's the size of population okay so a sample of size little n from a population of a size big n is obtained through simple random sampling if every possible sample of a size n has an equally likely chance of occurring the sample is then called a simple random sample okay so to obtain a simple random sample here is what we're going to do first we're going to list all individuals in the population and number them okay so if I want to obtain a simple random sample of let's say five students right I want to select five students from 35 students in our classroom so 35 students will be a population okay then I will put all of your names all 35 students names on like a roster and I will label your names like 1 through 35 okay so you list all individuals in the population in number data and that process is called frame process and the list of 35 students is called a frame then we randomly select an individual using random number generator process so we can use random number table or round int or Rand in no rep on ti-84 calculator so we can get random numbers from a random number table that's gonna be covered in the next video and also we can use a random number generator on our calculator that is also in the next video okay so more about these later random number table and the calculator random number function are great but we can also pull numbers out of a hat you know because that's technically leaving up to chance and every number we pull out of the hat has an equally likely chance of occurring so that's okay too all right so we do that which is randomly select and individual using one of these methods right until the sample size and you want okay so you're going to repeat the same thing until the sample size and you want now this process is called sampling without replacement okay in a sample without replacement an individual who is selected already is removed from the population and cannot be chosen again right so you choose one person the same person it cannot be chosen again okay okay so let's take a look at an example so mrs. Forbes has four friends Alice Bonnie Katherine and Susie and she wants to take two of them to the movies okay question a list all possible samples of size n equals two from the population of size N equals four okay so we have a sample size of a two and a population size of four it makes sense we have one two three four people right so that's N equals four and we're choosing two of them okay so the little n will be 2 all right once an individual is chosen she can now be chosen again okay so that's a sample without the replacement right all right so I could take Alice and Bonnie or I could choose Alice and Katherine okay or I could choose Alice and Susie hey or we can choose Bonnie and how about Bonnie and Alice you guys start with a Bonnie and then next one is Alice well I'm nothing when I do that because I already have that here right Alice and Bonnie Ambani and Alice same thing okay same two people so I'm not they're gonna write that selection okay so Bonnie and who Katherine okay and I can choose funny and Susie okay and also I can choose Katherine and Susie okay that's it so we have a six possible samples of a size n equals two okay so we have one two three four five six alright that's it for Part A Part B comment on the likelihood of the sample containing Bonnie and Suzy okay so since this is a simple random sample each sample is equally likely to happen and notice that we have one sample that contains Bonnie and Suzy right one out of six basically okay so what we need to say here is that only one out of the six possible samples contains Bonnie and Suzy so there is a 1 out of 6 1 / 6 1 / 6 chance that the simple random sample will contain Bonnie and Suzy okay and that's it alright so that's it for this video I'm gonna see you in the next one bye guys