Question Video: Determining Which Sampling Method Is Simple Random Sampling | Nagwa Question Video: Determining Which Sampling Method Is Simple Random Sampling | Nagwa

# Question Video: Determining Which Sampling Method Is Simple Random Sampling Mathematics • First Year of Preparatory School

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A restaurant owner wants to know if his guests enjoyed the food served in one evening. He decides to ask some of his guests. He chooses a sample. Which of the following methods is considered a random sampling method? [A] Choosing those who sit at tables that have even numbers [B] Choosing female guests [C] Choosing those who order chicken [D] Choosing male guests [E] Choosing those who enter the restaurant after 11 PM

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### Video Transcript

A restaurant owner wants to know if his guests enjoyed the food served in one evening. He decides to ask some of his guests. He chooses a sample. Which of the following methods is considered a random sampling method? Option (A) choosing those who sit at tables that have even numbers. Option (B) choosing female guests. Option (C) choosing those who order chicken. Option (D) choosing male guests. Or option (E) choosing those who enter the restaurant after 11 PM.

We’re given five different ways of taking a sample of the guests in a restaurant, that is, five sampling methods. And we’re asked which of these can be considered a random sampling method. So let’s begin by defining what we mean by a random sampling method. We remind ourselves first that a population is defined as the entire set of objects we’re analyzing or concerned with. In our case then, we can say that the population is all of the restaurant’s guests on the evening in question. We then define a sample as a smaller subset or a selection of the population. A random sample, sometimes classed as a simple random sample, is a sample where every member of the population has an equal chance, or probability, of selection. The sampling method is the method we use to select the sample members from the population.

Let’s consider each of the methods given in options (A) to (E), starting with option (A). This sampling method selects guests who sit at tables that have even numbers. Assuming that guests were seated randomly at the tables in the restaurant on arrival, there should be nothing to distinguish between guests who sit at even-numbered tables and those who sit at odd-numbered tables. Since guests are equally likely to have been allocated an even-numbered table as an odd one to sit at, the method described in option (A) can be considered a random sampling method.

Now let’s consider option (B), where the sampling method is to choose female guests. If our sampling method selects only female guests, then any male guests will have zero chance of selection. The selection is therefore not random, since we’re excluding any male guests completely from the sample. Therefore, option (B) cannot be considered a random sampling method. Noting that the same logic applies in option (D), where instead of female guests, only male guests are chosen, we can also discount option (D). Option (D) cannot be considered a random sampling method.

Now let’s go back and look at option (C). In option (C), only guests who order chicken are selected. Now if this were a restaurant where the only thing served was chicken, we could then say that taking a sample of those guests who order chicken would be considered a random sample. But we’re not given any information as to what’s on the menu. So we can’t assume that only chicken is served. Then choosing only guests who order chicken means that anyone who does not order chicken has no chance of being selected. All guests do not have an equal chance of being selected, so the sampling method is not random and we can discount option (C).

Finally, considering option (E), where only guests entering the restaurant after 11 PM are chosen, this excludes any guests who enter the restaurant before 11 PM. All of those guests have zero chance of being selected, and the chance of being selected is not equal for every member of the population of guests. This sampling method cannot therefore be considered as a random sampling method. And so we can eliminate option (E).

Hence, option (A), that is, choosing those guests who sit at tables that have even numbers, is the only sampling method that is considered random.

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