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) False because P(A or B) = P(A) + P(B) - P(A and B). Therefore, P(A and B) = P(A) + P(B) - P(A or B).

(b) True because variance = 0 means all values are same as mean value. Therefore, all the observations in this data set are identical.

(c) True, normal distribution is a bell shaped curve distribution and mean = median = mode. The normal curve is symmetrical about its mean.

(d) False because first curve has smaller standard deviation so less spread.

(e) True because p-value < 0.05. Therefore, we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.

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