True or False. Justify for full credit. (a)If A and B are any two events, then P
ID: 3181055 • Letter: T
Question
True or False. Justify for full credit.
(a)If A and B are any two events, then P(A AND B) P(A OR B).
(b)If the variance of a data set is 0, then all the observations in this data set must be identical.
(c)A distribution may have more than one mode.
(d)When plotted on the same graph, a distribution with a mean of 60 and a standard deviation of 5 will look more spread out than a distribution with a mean of 40 and standard deviation of 8.
(e)In a left-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
Solution:-
(a) True, If A and B are any two events, then P(A AND B) P(A OR B).
(b) True, If the variance of a data set is 0, then all the observations in this data set must be identical.
(c) True, A distribution may have more than one mode.
(d) False, When plotted on the same graph, a distribution with a mean of 60 and a standard deviation of 5 will look more spread out than a distribution with a mean of 40 and standard deviation of 8.
The spread of the plotted grapg depends on standard deviation, the standard deviation of the second distribution is larger hence the spread would also be larger.
(e) True, In a left-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.
Since p value(0.03) is less than the significance value 0.05, so we have to reject the null hypothesis.
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