True or False. Justify for full credit. (a) The standard deviation of a data set

Question

True or False. Justify for full credit.

(a) The standard deviation of a data set cannot be negative.

(b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.2.

(c) The mean is always equal to the median for a normal distribution.

(d) A 95% confidence interval is wider than a 98% confidence interval of the same parameter.

(e) In a two-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows

a Student’s t-distribution with P(T < 1.5) = 0.98, then we fail to reject the null hypothesis at 0.05 level of significance .

Explanation / Answer

a) False, Standard Devaition is the square root of Variance. Variance is a non-negative quantity

b) True, If A and B are disjoint, then A and B are independent. So P(A intersection B) = P(A) * P(B)

PA and B) = P(A intersection B)

c) True, Normal distribution is symmetric about mean.

d) True, 98% hold larger population, and it has more accuracy

e) True, P value is greater than level of significance

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