O A. Ho: Ốc = Ec and Op = Ep and Ow =Ew H,: Oc #Ec or Op #Ep or Ow #Ew B. Ho: Gender and drop reason are independent. H,: Gender and drop reason are dependent. OC. Ho: Pc = Pp = Pw H,: At least one of the proportions is different
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
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A survey of 36 randomly selected students who dropped a course was conducted at a college. The
following results were collected. Complete parts (a) through (c).
(b) Test whether gender is independent of drop reason at the a = 0.1 level of significance.
Full data set O
M Course M
M Course F
M
M Personal F Course F
F Course M
M PersonalF Personal M
Work
Course
What are the hypotheses?
Work
Personal
Work
Work
Personal
O A. Ho: Oc = Ec and Op = Ep and Ow = Ew
H7:0c #Ec or Op #Ep or Ow #Ew
Course
M Course
Course
Course
B. Ho: Gender and drop reason are independent.
M Course F
M
Work
Course
H,: Gender and drop reason are dependent.
F Personal F
F Personal F Course M
Work
Work
Course
Work
O C. Ho: PC = Pp = Pw
F Personal F
M
Work
H: At least one of the proportions is different from the others.
F
F Course M Course F
Work
Work
Personal
Work
Calculate the test statistic.
(Round to three decimal places as needed.)"
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