In the following situations assume that half of the specified population is male

Question

In the following situations assume that half of the specified population is male and the other half is female. (a) Suppose you're sampling from a room with 10 people. What is the probability of sampling two females in a row when sampling with replacement? What is the probability when sampling without replacement? (b) Now suppose you're sampling from a stadium with 10,000 people. What is the probability of sampling two females in a row when sampling with replacement? What is the probability when sampling without replacement? (c) We often treat individuals who are sampled from a large population as independent. Using your findings from parts (a) and (b), explain whether or not this assumption is reasonable.

Explanation / Answer

Solution:-
a) 4/9 = 0.4444

b) 4999/9999 = 0.4999

c)Yes,it is reasonable. In a large population,when doubtless the sample size is a small- scale percentage of the population,it makes very little difference whether the sampling is done with or without replacement

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