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 identical.
(c) There may be more than one mode in a data set.
(d) A 90% confidence interval is wider than a 95% confidence interval of the same parameter.
(e) In a right-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

A) True, as P(A) + P(B) -P(A and B) = P(A or B)

from given value P(A and B) is zero, so this means that A and B are disjoint.

B) True,

The variance of a constant random variable is zero, and if the variance of a variable in a data set is 0, then all the entries have the same value: As Variance is invariant with respect to changes in a location parameter.

C) True,

It is possible for a set of data values to have more than one mode. If there are two data values that occur most frequently, we say that the set of data values is bimodal. If there is no data value or data values that occur most frequently, we say that the set of data values has no mode.

D) False,

A 90% Confidence Interval would be narrower than a 95% Confidence Interval. This occurs because the as the precision of the confidence interval increases (ie CI width decreasing), the reliability of an interval containing the actual mean decreases (less of a range to possibly cover the mean)

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