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 OR B) = 0.9 (b) If the variance for a data set is zero, then all the observations in this data set must be zero. (c) There may be more than one mode in a data set. (d) A 98% confidence interval is wider than a 95% 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. -3 -2

Explanation / Answer

Answer to the question is as follows:

1. Two sets are said to be disjoint if they have no element in common. So, P( A or B) = P(A)+P(B) - P(A and B) = .4+.5-0 = .9. So, TRUE

2. Variance is 0, then the obs need not be all zero. they just need to be all equal
False

3. Yes, TRUE. Higher confidence mean more interval

4. False. In a 2 tailed hypothesis the alpha is distributed in 2 tails. So each tails. has .025. Since shaded area of .03 is more than .025 we conclude that we do not have sufficient eveidence to reject the null hypothesis

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