It is believed that 11% of all Americans are left-handed. A college needs to know the number of left-handed desks to place in the large instructional lecture halls being constructed on its campus. In a random sample of 350 students from that college, whether or not a student was left-handed is recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a different percentage of left-handers than the general American population. State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem.
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.
It is believed that 11% of all Americans are left-handed. A college needs to know the number of left-handed desks to place in the large instructional lecture halls being constructed on its campus. In a random sample of 350 students from that college, whether or not a student was left-handed is recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a different percentage of left-handers than the general American population. State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem.
- The wording for the parameter in context is as follows:
- Fill in the correct null and alternative hypotheses.
H0:H0:
HA:HA: - A Type I error in the context of this problem would be
- A Type II error in the context of this problem would be
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