Use the following for questions 14-17: One student is selected at random from a

Question

Use the following for questions 14-17: One student is selected at random from a group of 200 known to consist of 140 full-time (80 female and 60 male) students and 60 part-time (40 female and 20 male) students. Let A be the event "the student selected is full-time," and let C be the event "the student selected is female." 14. Fill in the four areas of the Venn Diagram below 15. What is the probability that the student selected is neither a full-time student nor a female? A· 0.5 B. 0.3 C. 0.2 D. 0.1 16. Given that the person selected at random is female, what is the probability that they are a full-time student? A. 0.67 B.0.40 C. 0.75 D.0.57 17. Events A and C are: A. C. Disjoint and Independent Joint and Dependent B. Joint and Independent D. Disjoint and Dependent 18 Suppose we conduct a two-sided hypothesis test of a sample of size 21 and we use a significance level of -0.05. We calculate the test statistic to be ta-1.90. Which of the following is correct? A. 0.025p-value

Explanation / Answer

14)A- full time
C - female
P(A and C )= 80/200 = 0.4
P(A - C) = (140 - 80)/200 = 0.3
P(C -A) = 0.2
P(not A and not C) = 0.1

15) P(not A and not C) = 0.1

16) P(A|C) = P(A and C)/P(C) = 0.4/0.6 = 2/3
17)
C) joint and dependent
as P(A and C) not equal to 0 and P(A|C) not equal to P(A)

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