A realtor studies the relationship between the size of a house (in square feet) and the property taxes (in $) owed by the owner. The table below shows a portion of the data for 20 homes in a suburb 60 miles outside of New York City. [You may find it useful to reference the t table
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.
Tree diagram
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 realtor studies the relationship between the size of a house (in square feet) and the property taxes (in $) owed by the owner. The table below shows a portion of the data for 20 homes in a suburb 60 miles outside of New York City. [You may find it useful to reference the t table.]
| Property Taxes | Size | ||||
| 21,872 | 2,464 | ||||
| 17,498 | 2,451 | ||||
| ⋮ | ⋮ | ||||
| 29,294 | 2,895 | ||||
Click here for the Excel Data File
a-1. Calculate the sample
a-2. Interpret rxy.
multiple choice 1
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The correlation coefficient indicates a positive linear relationship.
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The correlation coefficient indicates a negative linear relationship.
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The correlation coefficient indicates no linear relationship.
b. Specify the competing hypotheses in order to determine whether the population correlation coefficient between the size of a house and property taxes differs from zero.
multiple choice 2
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H0: ρxy = 0; HA: ρxy ≠ 0
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H0: ρxy ≥ 0; HA: ρxy < 0
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H0: ρxy ≤ 0; HA: ρxy > 0
c-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
c-2. Find the p-value.
multiple choice 3
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p-value < 0.01
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p-value0.10
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0.05p-value < 0.10
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0.02p-value < 0.05
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0.01p-value < 0.02
d. At the 5% significance level, what is the conclusion to the test?
multiple choice 4
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Reject H0; we can state size and property taxes are correlated.
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Reject H0; we cannot state size and property taxes are correlated.
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Do not reject H0; we can state size and property taxes are correlated.
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Do not reject H0; we cannot state size and property taxes are correlated.
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