True or False. Justify for full credit. (a) If A and B are any two events, then

Question

True or False. Justify for full credit.

(a) If A and B are any two events, then P(A AND B) = P(A) + P(B).

(b) If the variance of a data set is 0, then all the observations in this data set must be identical.

(c) A normal distribution curve is always symmetric to its mean.

(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

(a) If A and B are any two events, then P(A AND B) = P(A) + P(B). ;; false

(b) If the variance of a data set is 0, then all the observations in this data set must be identical. true

c)c) A normal distribution curve is always symmetric to its mean. true

d)(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. :false as spread is proportional to SD

e)(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. ; true

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