True or False (a) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A

Question

True or False

(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)

Since events A and B are disjoint so P(A and B) = 0.

P(A or B) = P(A) + P(B) - P(A and B) = 0.4+0.5 = 0.9

Answer: True

(b)

When all the observations are same then also the variance of a data set is zero. So

Answer : false

(c)

For normal distribution mean, median and mode are same.

Answer : true

(d)

As the significance level decreases, critical value increases , so it is difficult to reject the null hypothesis.

Answer : false

(e)

2 P(T > 2) = 0.06

Since p-value is greater than 0.05 so we have not sufficient evidence to reject the null hypothesis at 0.05 level of significance.

Answer : false

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