True o r False . Justify for full credit. (a) The standard deviation of a data s

Question

True o r False . Justify for full credit. (a) The standard deviation of a data set cannot be negative. (b) If P(A) = 0.4 , P(B) = 0.5 , and A and B are disjoint , then P(A AND B) = 0. 2 . (c) The mean is always equal to the median for a normal distribution . (d) A 9 5 % confidence interval is wider than a 9 8 % confidence interval of the same parameter . (e) In a two - tailed test, the value of the test statistic is 1.5. If we kno w the test statistic follows a Student’s t - distribution with P (T < 1.5) = 0 .9 8 , then we fail to reject the null hypothesis at 0 .05 level of significanc e .

Explanation / Answer

(a) The standard deviation of a data set cannot be negative. TRUE, a square root value can not be negative.

(b) If P(A) = 0.4 , P(B) = 0.5 , and A and B are disjoint , then P(A AND B) = 0. 2 .FALSE, if the two event are disjoint then P(A and B)=0

(c)(c) The mean is always equal to the median for a normal distribution .TRUE, the normal distribution is symetric about its mean, median and mode.

(e) In a two - tailed test, the value of the test statistic is 1.5. If we kno w the test statistic follows a Student’s t - distribution with P (T < 1.5) = 0 .9 8 , then we fail to reject the null hypothesis at 0 .05 level of significance .TRUE, the P value is greater than alpha. so fail to reject the null.

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