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.] a-1. Calculate the sample correlation coefficient rxy. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) a-2. Interpret rxy. multiple choice 1 The correlation coefficient indicates a positive linear relationship. The correlation coefficient indicates a negative linear relationship. 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 H0: ρxy = 0; HA: ρxy ≠ 0 H0: ρxy ≥ 0; HA: ρxy < 0 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 p-value < 0.01 p-value > and equal to 0.10 0.05 < and equal to p-value < 0.10 0.02 < and equal to p-value < 0.05 0.01 < and equal to p-value < 0.02 d. At the 5% significance level, what is the conclusion to the test? multiple choice 4 Reject H0; we can state size and property taxes are correlated. Reject H0; we cannot state size and property taxes are correlated. Do not reject H0; we can state size and property taxes are correlated. Do not reject H0; we cannot state size and property taxes are correlated.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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.]
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-value > and equal to 0.10
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0.05 < and equal to p-value < 0.10
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0.02 < and equal to p-value < 0.05
- 0.01 < and equal to p-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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