True or False. Justify for full credit. (a) If P(A) = 0.4 , P(B) = 0.5, and A an

Question

True or False. Justify for full credit.       
(a) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A OR B) = 0.9.

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

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

(d) It’s easier to reject the null hypothesis at significance level of 0.01 than at significance level of 0.05. (e) In a two-tailed test, the value of the test statistic is 2. If we know the test statistic follows a Student’s t-distribution with P(T >2) = 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 disjoint, probability of A OR B is : P(A)+P(B)=0.4+0.5=0.9 [True]

b) Variance: 1/N Summation (Xi-Xbar)^2, if variance is zero, then all the observations in data set is zero. [true]

c) For normal distribution, the value of average and middle most value is always same. [True]

d) If the null hypothesis is rejected at 0.01, it is evident that it will be rejected at alpha=0.05 too. [true]

e) The p value is less than 0.05. Therefore, reject null hypothesis. [true]

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