Two schools are investigating whether there is a difference in the proportion of students who attend the homecoming football game. Both schools have over 2,000 students. School A selected a simple random sample of 100 students and found that 98 attended the homecoming football game. School B selected a simple random sample of 150 students and found that 142 attended the homecoming football game. Let pˆc represent the combined sample proportion for the two schools, and let nA and nB represent the respective sample sizes. Have the conditions for statistical inference for testing a difference in population proportions been met? No, the condition for independence has not been met, because random samples were not selected from both schools. A No, the condition for independence has not been met, because the sample sizes are too large when compared to the corresponding population sizes. B No, the condition that the distribution of the difference in sample proportions is approximately normal has not been met, because nA(pˆc) is not greater than or equal to 5. C No, the condition that the distribution of the difference in sample proportions is approximately normal has not been met, because nA(1−pˆc) is not greater than or equal to 5. D All conditions for making statistical inference have been met.
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.
Two schools are investigating whether there is a difference in the proportion of students who attend the homecoming football game. Both schools have over 2,000 students. School A selected a simple random sample of 100 students and found that 98 attended the homecoming football game. School B selected a simple random sample of 150 students and found that 142 attended the homecoming football game. Let pˆc represent the combined sample proportion for the two schools, and let nA and nB represent the respective
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No, the condition for independence has not been met, because random samples were not selected from both schools.
A -
No, the condition for independence has not been met, because the sample sizes are too large when compared to the corresponding population sizes.
B -
No, the condition that the distribution of the difference in sample proportions is approximately normal has not been met, because nA(pˆc) is not greater than or equal to 5.
C -
No, the condition that the distribution of the difference in sample proportions is approximately normal has not been met, because nA(1−pˆc) is not greater than or equal to 5.
D -
All conditions for making statistical inference have been met.
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