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The representative part of Population is called Sample.

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Difference between sampling with replacement and without replacement?

http://www.ma.utexas.edu/users/parker/sampling/repl.htm


When sampling without replacement should you use multiplication rule for independents or dependents events?

hell no nigaa


What does it mean when sampling is done without replacement?

Once an individual is selected, the individual cannot be selected again.


Is sampling with replacement a finite population?

no


When you sample with replacement are the trials independent?

They are, if the sampling and replacement processes don't introduce any bias.


Why is simple random sampling without replacement preferred over simple random sampling with replacement?

Simple random sampling without replacement is often preferred because it ensures that each selected individual is unique, which can lead to a more representative sample of the population. This method helps to avoid over-representation of certain individuals and can provide more accurate estimates for population parameters. Additionally, it reduces the variability in sample statistics, making it easier to generalize findings to the larger population. Overall, this method enhances the reliability of the results while maintaining the randomness of the selection process.


As defined in the text random sampling requires sampling with replacement?

Not necessarily. A random sample can occur with or without replacement, depending on what makes more sense. For instance, trying to calculate the odds of a dice roll would require a random sample with replacement (because it is perfectly possible to get a 6 on each and every die); trying to calculate the odds of a poker hand, however, would require random sampling without replacement (the ace of spades can only show up once in any given round of dealing). when the population size is large enough, the difference between the two is meaningless; people who make national surveys, for instance, usually choose people randomly without replacement (there's no possibility they will survey the same person twice) but treat it as though the were sampling with replacement (because the math is easier). The only requirement for a random sample is that each object that might be chosen has a known and well-defined probability of being chosen at any given moment. For random samples with replacement that probability is always the same; For random samples without replacement that probability is determined by the objects that have previously been selected.


Two cards are drawn from a deck of cards. what is the probability that both cards are spades?

This question is a little bit tricky. In a deck of 52 cards, one-fourth or 13 cards are spades. So, the chance of drawing one spade = 13/52 or 0.25. If a second card drawn, there's one less spade in the deck, so the probability on the second draw is 12/51. The probability of drawing two spades from a deck is 0.25 x 12/51 = 0.058824 This is called sampling without replacement. In quality control, it is very common to sample without replacement as bad parts are discarded. If we consider drawing one card, putting it back in the deck, regardless if it is a spade or not, then reshuffling the deck and drawing the second card, the probability is 0.25 x 0.25 = 0.0625, a bit higher with replacement. This is the same as 1/4 x 1/4 = 1/8 or saying the odds are 1:8. I've included a couple of links on sampling with replacement and without replacement. Generally, for calculating statistics, we attempt to get independent results. The draw of one card, will reduce the population, and change the probabilities on the second draw, so sampling without replacement is not independent sampling. See related links.


Why is sampling with replacement used?

Sampling with replacement is used when it is desirable for each item in the population to have an equal chance of being selected each time, and when it is acceptable for the same item to be selected multiple times in the sample. This method is commonly used in bootstrap resampling and in situations where the population is large and well-mixed.


What is population sampling?

Population sampling is the process in which a group of individuals are selected to represent a population for the purpose of statistical analysis. Population sampling allows the analyzers to learn about a population without studying every individual in it.


What does the word without replacement mean?

"Without replacement" refers to a sampling method in which an item is selected from a set and then not returned to the set before the next selection. This means that each subsequent selection is made from a reduced pool of items, affecting the probabilities of choosing each item. This concept is commonly used in statistics and probability theory, particularly in scenarios involving drawing cards from a deck or selecting objects from a collection.


How many samples of size 5 are possible when selecting from a set of 10 distinct integers if the sampling is done with replacement?

105 or 100,000

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