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Chapter 7: Problem 20

Assume your class has 30 students and you want a random sample of 10 of them. A student suggests asking each student to flip a coin, and if the coin comes up heads, then he or she is in your sample. Explain why this is not a good method.

Short Answer

Expert verified
The coin-flip method is not suitable for selecting 10 students from a total of 30 as it is not designed to select an exact number of students. Also, there could be an imbalance in the selection, leading to more or less than the desired number of students being selected, violating fairness and randomness.

Step by step solution

01

Identify the Main Issue with the Method

Let's imagine the proposed method: Each student flips a coin, if the coin lands on 'heads', he or she is selected, if it lands on 'tails', the student is not. What may seem like an issue immediately here? The problem with this method is that the exact desired number of 10 students is not guaranteed. Depending on the coin flips, there could be more or less than 10 students in the sample.
02

Explain the Principle of Probability

The chance of getting heads in a fair coin flip is 0.5. Since we have 30 students each tossing the coin, we would expect roughly half of them, or 15 students, to land on heads. That is already more students than our desired sample size of 10 students. Additionally, because these are independent events, there is a chance that less than 10 or even more than 15 students could land on heads.
03

Comparison with Proper Random Sampling Method

In a proper random sampling like drawing names from a hat or a number generator, each student would have an equal and known chance of being selected, and we can control the exact number of selected students. The proposed coin-flip method doesn't have these properties, and therefore it doesn't guarantee a balanced and fair selection process. It may lead to small or large samples, and this unpredictability makes it an unsuitable method.

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