IGNOU AST 1 2018 - State whether the following statements are true or false. Give brief j

Question

State whether the following statements are true or false. Give brief justification.
a) The number of samples of size 3 with replacement from a population of size 6 is 20.
b) If the odds in favour of an event A are 3 : 4, then the probability of occurrence of A
will be 4/7.
c) If the level of significance is the same, the area of the rejection region in a 2-tailed
test is less than that in a 1-tailed test.
d) There is no seasonal variation in an annual time series.
e) In a binomial distribution, if X represents the number of successes in 25 trials and the
probability of success at each trial is 0.5, then the standard deviation of X is 2.

07 Mar 2018

Answer :

Word Count : 543

a) The number of samples of size 3 with replacement from a population of size 6 is 20.
False. The number of samples of size 3 with replacement from a population of size 6 is not 20. When sampling with replacement, each selection is independent, and for each of the 3 selections, you have 6 choices (since you replace the item after each selection). So, the total number of possible samples is 6 * 6 * 6, which is 216, not 20.

b) If the odds in favor of an event A are 3 : 4, then the probability of occurrence of A will be 4/7.

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