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# 1. True or False. Justify for full credit. (25 pts)(a) If all the

observations in a data set are identical, then the variance for this data set iszero.(b) If P(A) = 0.4 and P(B) = 0.5, then P(A AND B) = 0.2.(c) The mean is always equal to the median for a normal distribution.(d) A 95% confidence interval is wider than a 90% confidence interval of the sameparameter.(e) In a two-tailed hypothesis testing at significance level α of 0.05, the test statistic iscalculated as 2. If P(X &gt;2) = 0.03, then we have sufficient evidence to reject the nullhypothesis.

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(a) If all the observations in a data set are identical, then the variance for this data set is
zero.
Solution:
If there is n y1, y2,……,yn observation then the variance is...

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