A city is collecting data on two neighborhoods, one low income and one middle income, to see whether or not their residents would support an increase in local sales tax to pay for more city services. The city wishes to see if there is evidence to show that the first neighborhood (low income) has a lower level of support for the tax compared to the second neighborhood (middle income). You wish to test the following claim (HaHa) at a significance level of α=0.002 Ho:p1=p2 Ha:p1
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 city is collecting data on two neighborhoods, one low income and one middle income, to see whether or not their residents would support an increase in local sales tax to pay for more city services. The city wishes to see if there is evidence to show that the first neighborhood (low income) has a lower level of support for the tax compared to the second neighborhood (middle income).
You wish to test the following claim (HaHa) at a significance level of α=0.002
Ho:p1=p2
Ha:p1<p2
You obtain a sample from the first population with 219 successes and 131 failures. You obtain a sample from the second population with 177 successes and 53 failures.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
The p-value is...
- less than (or equal to) αα
- greater than αα
This test statistic leads to a decision to...
- reject the null
- accept the null
- fail to reject the null
As such, the final conclusion is that...
- There is sufficient evidence to reject that the first neighborhood (low income) has a lower level of support for the tax compared to the second neighborhood (middle income).
- There is not sufficient evidence to reject that the first neighborhood (low income) has a lower level of support for the tax compared to the second neighborhood (middle income).
- There sufficient evidence to support that the first neighborhood (low income) has a lower level of support for the tax compared to the second neighborhood (middle income).
- There is not sufficient evidence to support that the first neighborhood (low income) has a lower level of support for the tax compared to the second neighborhood (middle income).
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