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# 10% Rule of assuming "independence" between trials

10% Rule of assuming "independence" between trials.

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• doesn't this mean drawing cards in a deck of cards without replacing can be binomial if my number of trials is less than 5?
• I understand that it won't be binomial per definition, but can be treated as if it was because the results will be close enough to the precisely calculated numbers.
• How does the 10% rule make sense? The 10% rule says that if my sample size is less than 10% of the population, then I can assume independence. Isn’t this counterintuitive? Why does taking a smaller sample size result in a more accurate probability?
• Hi Rishabh,
A smaller sample size does not result in a more accurate probability, but rather results in the ability to assume independence, which then allows us to make some useful inferences about the results. Sal touches on this during the last minute.
Hope this helped. You can learn anything!
~Dayvyd
• why is 10% chosen? what advantage does it have over other percentages?
• The main idea here is that because as the proportion of the sample size over the population approaches 0, it behaves more like binomial distribution. So people might want to make a rule of thumb to use the assumption of independence. There's no particular reason to choose why 10% as why don't we choose 11% or 9%. It depends on the statistician's preference to accuracy. One possible reason to favor 10% is because it's easier to compute 10% of a number than, let say, 8%. Hope that helps! CMIIW
• what are the properties of normal distribution? there is no video till now on it , to best of my knowledge. Plz provide me link if there is so.
(1 vote)
• Here are some properties of the normal distribution.

1. The normal distribution is symmetric about its only peak. The peak is located at the mean, median, and mode, which are all equal.

2. The probability is approximately 68% that the score is within 1 standard deviation from the mean (in either direction), approximately 95% that the score is within 2 standard deviations from the mean, and approximately 99.73% that the score is within 3 standard deviations of the mean.

3. Any linear combination of any number of independent normally distributed random variables is also normally distributed.

4. For a sufficiently large number of independent random variables with a common distribution (not necessarily normal) with finite mean and finite nonzero variance, the sample mean is approximately normally distributed.
• Does the 10% rule apply to a randomized experiment?
• Yes, the 10% rule can apply to randomized experiments as well, particularly when the experiment involves sampling from a larger population. The rule helps assess whether the sample size is sufficiently small relative to the population size to justify assuming approximate independence between trials.
• So does the 10% condition take into account future population? I'm analyzing data from all 29 kids in my senior class and we're a small school, so this is more than 10% of seniors who have gone to my school, but less than 10% of all seniors who will ever go to my school. Does that qualify or not?
• The 10% condition typically refers to the current population size from which the sample is drawn, rather than considering future populations. In your scenario, if you're analyzing data from all 29 kids in your senior class, and that represents more than 10% of the current seniors at your school but less than 10% of all seniors who will ever attend your school, it would still qualify for the 10% condition. The condition is based on the current population size to assess whether the sample size is reasonably small relative to that current population.
(1 vote)
• In this example what was the sample size?
• The mall example would be 10,000, thee class example would be "n"
• In the example that Sal explains at the beginning about a mall, if there is people entering the mall while we sample the people that leave the mall, we shouldn´t mind about the 10% rule right? Because this way is as if there was replacement.
(1 vote)
• Keep in mind that it's likely the person entering the mall would give a different answer than the person exiting. This could potentially make the difference between w/o and w/ replacement even greater than in the case where no one could enter.
(1 vote)
• the video refers to the rule of independence but doesn't that rule just mean that the outcome of one trial doesn't affect the outcome of another?
i feel like the right rule this relates to is the one that states that the probability of success must be constant (which is usually what replacement affects)
maybe that was just an oversight but that was a bit confusing
(1 vote)
• You're correct that the rule of independence typically refers to the condition where the outcome of one trial does not affect the outcome of another. This is indeed related to the concept of independence in probability theory. The replacement aspect often affects the constancy of the probability of success on each trial, which is another important consideration for binomial distributions. While the video may have simplified by referring to the "rule of independence," it encompasses both the idea of trials being independent and the constancy of the probability of success on each trial.
(1 vote)
• why is it important for our trials to be independent in a binomial varible?
(1 vote)
• if the trials are independent, you can reasonably assume that the random variable is binomial
(1 vote)