10. Continuing with the same population in Question 7, let us consider the case where we...

10. Continuing with the same population in Question 7, let us consider the case where we picked a sample of size 14. (Do not worry

about the fact that it is stupid to have a sample of size 14 when the population has only 4 people in it.) What is the standard error

(deviation) of the sampling distribution of the mean?

11. You need to clean out a fish tank, so you get a small bowl to take out all the fish one at a time. You have 20 betta fish and 5 gold

fish. Assuming that each fish in the tank has an equal likelihood of being taken out, is the probability of getting a certain number of betta

fish in the first four draws a binomial distribution? Please explain.

Expert Solution

Q10

Standard error (deviation) of the sampling distribution of the mean

= (Population Standard deviation)/√14 ANSWER

[unable to provide a numerical answer since Population Standard deviation is not indicated in ht equestion]

Q10

No, it will not be a Binomial Distribution. It will be a case of Hypergeometric Distribution.

Suppose the number of fish in the tank is n, of which k are of beta fish and p is the probability of getting a beta fish in any draw.

Since fish are taken out one at time, p = k/n for the first draw, but p = (k - 1)/(n - 1). Thus, p does not remain constant from draw to draw.

Important condition for application of Binomial Distribution is that p should remain constant over the draws.

In this case, Hypergeometric Distribution is most appropriate. ANSWER

[Going beyond, if the draws were with replacement, then the distribution is Binomial. Also, if n is considerably large in comparison to k so that (k/n) is virtually equal to {(k - 1)/(n - 1)}, Binomial can be applied]

orchestra answered 1 year ago

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