Question

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.

Answer 1

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]