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

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Q: When you sample with replacement are the trials independent?
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In a controlled experiment how do the number of trials and sample sizes effect the results?

The number of trials and sample sizes generally increase the accuracy of the results because you can take the average or most common results in the experiment


How do you get relative frequency?

The relative frequency of an event, from repeated trials, is the number of times the event occurs as a proportion of the total number of trials - provided that the trials are independent.


What is the type of variable that is kept the same for all the trials?

Independent Variable


What term defined as the size of the association between two variables independent of the sample size?

There is no such term. The regression (or correlation) coefficient changes as the sample size increases - towards its "true" value. There is no measure of association that is independent of sample size.


What are the assumptions underlying the two-sample t-test?

normal, SRS, independent normal, SRS, independent


What is sampling without replacement?

The representative part of Population is called Sample.


What is an independent value?

sample data drawn from one population is completely unrelated to the selection of sample data from the other population.


What is independent values?

sample data drawn from one population is completely unrelated to the selection of sample data from the other population.


What is she binomial probability distribution is used with?

It is used when repeated trials are carried out , in which there are only two outcomes (success and failure) and the probability of success is a constant and is independent of the outcomes in other trials.


Is binomial distribution is characterized by situations that are analogous to coin tossing?

Yes it is. For a binomial, there must be a fixed number of trials, the probability must remain constant for trials, trials must be independent, and each outcome must be classified into 2 categories.


Why do you use binomials?

Binomials are used when the total of n independent trials take place and one wants to find the probability of r successes, when each success has a probability "p" of occurring. There should be independent trails, Probability of success stays the same for all trials, Fixed number of trials and Two different classifications in order to use binomial distribution.


Does a binominal distribution with trials that are independent mean that the outcome of one trial does not affect the outcome of any other trial?

No. The fact that the outcome of one trial does not affect the outcome of any other trial follows from the fact that the trials that are independent. Whether the distribution is binomial or not is totally irrelevant.