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- A chi-square test for independence is being used to evaluate the relationship between two variables. If the hypothesis test has df = 3, what can a researcher conclude about the two variables? a. One variable consists of 2 categories, and the other consists of 3 categories. b. One variable consists of 2 categories, and the other consists of 4 categories. c. Both variables consist of 2 categories. d. Both variables consist of 3 categories.(4) 1. Let P(x) = "x is a good singer" and Q(x) = "x has appeared on The Voice." And the u.d. for x is all people. a. Translate into English Q(Samantha) v P(Samantha) b. Translate into symbols: There exists a person who is both a good singer and who has appeared on The Voice.Consider the following scenario: • Let P(C) = 0.4• Let P(D) = 0.5• Let P(C | D) = 0.6 Part (a) Find P(C AND D). Part (b) Are C and D mutually exclusive? Why or why not? A) There is not enough information to determine if C and D are mutually exclusive. B) C and D are not mutually exclusive because P(C AND D) ≠ 0 C) C and D are mutually exclusive because they have different probabilities. D) C and D are not mutually exclusive because P(C) + P(D) ≠ 1 . Part (c) Are C and D independent events? Why or why not? A) The events are independent because they are mutually exclusive. B) The events are not independent because P(C) × P(D) ≠ P(C | D) C) The events are not independent because P(C | D) ≠ P(C) D) The events are not independent because the sum of the events is less than 1. Part (d) Find P(D | C).
- 1)Suppose Z∼N(0,1). Calculate P(Z≤0.91). 2)Suppose Z∼N(0,1). Then P(Z>-1.6) is the same as:There is a chance that a bit transmitted through a digital transmission channel is received in error. Let X equal the number of bits in error in the next four bits transmitted. The possible values of X are {0,1,2,3}. Suppose that P(X=0)=0.6, P(X=1)= 0.3, P(X=2)= 0.05, P(X=3)= 0.05 What is the CDF of X at 3? i.e., what is F(3)? a). 0.6 b). 0.9 c). 0.95 d). 1 e). none of above For the random variable defined in question 12, if we know that Var(X)=0.6475, what is the standard deviation of X? a). 0.55 b). 0.6475 c). 0.419 d). 0.8 e). none of aboveWhat is the relationship between A = {xlx e N, x < 5} and B = {xlx e W greater than six but less than twelve} * The two sets are equivalent. The two sets are equal. O A is a subset of B. B is a subset of A.