A hypothesis examination is performed in a study of AirBnB's to learn about the proportion of them that have 4 televisions. The null and alternative hypotheses are as followed: Null: p=0.13 Alternative: p<0.13 Researchers had determined that 39/500 randomly selected airbnb's had 4 televisions. Once all of the necessary conditions were verified for a statistical inference, the researchers correctly calculated the P-Value to be approximately 2.7269x10^-4 a) If this hypothesis test is performed at the 1% level of significance, do the researchers reject the null hypothesis or fail to reject the nul hypothesis? Explain in a sentence or two. b) If this hypothesis tests is performed at the 1% level of significance, do the researchers reject the null hypothesis or fail to reject the null hypothesis? Explain in one to two sentences. c) If later it is revealed that the proportion of airbnb's that have four televisions is at least 0.13, describe whether the researchers made a type I or type II error with their conclusion in this hypthesis test (in reference to part a). If they made either a type I or a type II error, explain which kind of error they made and explain why in one to two sentences. If no error was made, explain in one to two sentences.
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.
A hypothesis examination is performed in a study of AirBnB's to learn about the proportion of them that have 4 televisions. The null and alternative hypotheses are as followed:
Null: p=0.13
Alternative: p<0.13
Researchers had determined that 39/500 randomly selected airbnb's had 4 televisions. Once all of the necessary conditions were verified for a statistical inference, the researchers correctly calculated the P-Value to be approximately 2.7269x10^-4
a) If this hypothesis test is performed at the 1% level of significance, do the researchers reject the null hypothesis or fail to reject the nul hypothesis? Explain in a sentence or two.
b) If this hypothesis tests is performed at the 1% level of significance, do the researchers reject the null hypothesis or fail to reject the null hypothesis? Explain in one to two sentences.
c) If later it is revealed that the proportion of airbnb's that have four televisions is at least 0.13, describe whether the researchers made a type I or type II error with their conclusion in this hypthesis test (in reference to part a). If they made either a type I or a type II error, explain which kind of error they made and explain why in one to two sentences. If no error was made, explain in one to two sentences.
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