True or False. Justify for full credit. (a) If A and B are disjoint, P(A) = 0.4

Question

True or False. Justify for full credit.

(a) If A and B are disjoint, P(A) = 0.4 and P(B) = 0.5, then P(A AND B) = 0.2.

(b) If all the observations in a data set are identical, then the variance for this data set is zero.

(c) There may be more than one mode in a data set.

(d) A 95% confidence interval is wider than a 98% confidence interval of the same parameter.

(e) In a two-tailed test, the value of the test statistic is 2. The test statistic follows a

distribution with the distribution curve shown below. If we know the shaded area is 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.

Explanation / Answer

Answer to this question is as follows:

In mathematics, two sets are said to be disjoint if they have no element in common.

a. If A and B are disjoint then P(A and B) = 0 irrespective what P(A) and P(B) are. So, a. is FALSE

b. If all points are same, then variance is 0. b. is TRUE

c. yes, such data are called multimodal distribution. c is TRUE

d. No. higher the confidence more is width. So, 98% confidence interval of same parameter is wider than that of 95%. d. is FALSE

e. Yes, since shaded area is less than level of significance of .05. Hence e. is TRUE.

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