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a) LAW OF LARGE NUMBERS say that if an experiment is repeated independently by large number of times, then sample mean approaches theoretical mean. So, (iii) cannot be accurate.
(ii) is accurate from if we go by definition mentioned above. (i) cannot be true is n is large as the distribution becomes normal. For all first n flips to be head, the distribution is poisson distribution. But, LLN states that when n is large all distribution tend to be normal distribution.
Thus, (ii) is the only CORRECT answer.
b) (i) and (iv) are the statements that are CORRECT. For clearer understanding , we use the following example.
Consider the null hypothesis (Ho) that a person is telling truth. Thus alternative hypothesis (Ha) is the person is lying.
The court gives a verdict of either "GUILTY" or "NOT GUILTY".
|NOT GUILTY||RIGHT||TYPE I ERROR (FALSE POSITIVE)|
|GUILTY||TYPE II ERROR (FALSE NEGATIVE)||RIGHT|
If the person is telling truth and court says " NOT GUILTY" then NO ERROR.
If the person is lying and court says "GUILTY" then NO ERROR.
If the person is telling truth and court says " GUILTY" then TYPE II ERROR or FALSE NEGATIVE as court failed to REJECT FALSE NULL HYPOTHESIS.
If the person is lying and court says "NOT GUILTY" then TYPE I ERROR or FALSE POSITIVE as court REJECTED TRUE NULL HYPOTHESIS.
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