Students at Hereford High School want to investigate whether they have more school spirit than students at Blake High School. To test this hypothesis, the students will select a random sample of students from each school and determine the proportion of the sampled students who wear school colors to their respective pep rallies. Let pHpH represent the proportion of Hereford students who wear school colors to their pep rally and pBpB represent the proportion of Blake students who wear school colors to their pep rally. Which of the following are the correct null and alternative hypotheses for the investigation? H0:pH−pB=0Ha:pH−pB≠0H0:pH−pB=0Ha:pH−pB≠0 A H0:pH−pB=0Ha:pH−pB>0H0:pH−pB=0Ha:pH−pB>0 B H0:pH−pB=0Ha:pH−pB<0H0:pH−pB=0Ha:pH−pB<0 C H0:pH−pB>0Ha:pH−pB=0H0:pH−pB>0Ha:pH−pB=0 D H0:pH−pB<0Ha:pH−pB=0
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.
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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.
Students at Hereford High School want to investigate whether they have more school spirit than students at Blake High School. To test this hypothesis, the students will select a random sample of students from each school and determine the proportion of the sampled students who wear school colors to their respective pep rallies. Let pHpH represent the proportion of Hereford students who wear school colors to their pep rally and pBpB represent the proportion of Blake students who wear school colors to their pep rally. Which of the following are the correct null and alternative hypotheses for the investigation?
-
H0:pH−pB=0Ha:pH−pB≠0H0:pH−pB=0Ha:pH−pB≠0
A -
H0:pH−pB=0Ha:pH−pB>0H0:pH−pB=0Ha:pH−pB>0
B -
H0:pH−pB=0Ha:pH−pB<0H0:pH−pB=0Ha:pH−pB<0
C -
H0:pH−pB>0Ha:pH−pB=0H0:pH−pB>0Ha:pH−pB=0
D -
H0:pH−pB<0Ha:pH−pB=0
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