True or False. Justify for full credit. (25 pts)

(a) The normal distribution curve is always symmetric to its mean.

True . this is because the mean, median and mode all lie about the same position.

(b) If the variance from a data set is zero, then all the observations in this data set are identical.

True. The variance is a measure of dispersion from the if the data set are identical then it would imply that the deviation from the mean is equal to zero.

C P(AANDA c )1, whereA c isthecomplementofA.

True. This is the case because the maximum probability in a given sample space is equal to if an element is not in thye sample space of A then it is in the complement of A. However the sum of the two sample spaces must always add up to 1.

dIn a hypothesis testing, if the p-value...