City Population City (in millions) Median age Chicago, IL 2.833 31.5 Dallas, TX 1.233 30.5 Houston, TX 2.144 30.9 Los Angeles, CA 3.849 31.6 New York, NY 8.214 34.2
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.
City planners believe that larger cities are populated by older residents. To investigate the relationship, data on population and median age in 10 large cities were collected.
| City | Population City (in millions) |
Median age |
| Chicago, IL | 2.833 | 31.5 |
| Dallas, TX | 1.233 | 30.5 |
| Houston, TX | 2.144 | 30.9 |
| Los Angeles, CA | 3.849 | 31.6 |
| New York, NY | 8.214 | 34.2 |
| Philadelphia, PA | 1.448 | 34.2 |
| Phoenix, AZ | 1.513 | 30.7 |
| San Antonio, TX | 1.297 | 31.7 |
| San Diego, CA | 1.257 | 32.5 |
| San Jose, CA | 0.930 | 32.6 |
Click here for the Excel Data File
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Draw a
scatter diagram .
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On the graph below, use the point tool to plot the point corresponding to the first Population City and its Median age(Population 1).
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Repeat the process for the remainder of the sample (Population 2, Population 3, … ).
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To enter exact coordinates, double-click on the point and enter the exact coordinates of x and y.
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Find the
correlation coefficient . (Round your answer to 3 decimal places.)
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A
regression analysis was performed and the resulting regression equation is Median age = 31.4 + 0.272 Population. Interpret the meaning of the slope.
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Estimate the median age for a city of 2.5 million people. (Round your answer to 2 decimal places.)
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Here is a portion of the regression software output. What does it tell you?
| Predictor | Coef | SE Coef | T | P |
| Constant | 31.3672 | 0.6158 | 50.94 | 0.000 |
| Population | 0.2722 | 0.1901 | 1.43 | 0.190 |
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f. Using the 0.10 significance level, test the significance of the slope. Interpret the result. Is there a significant relationship between the two variables?
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f-1. Choose the appropriate hypotheses.
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H0: β = 0 H1: β ≠ 0
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H0: β < 0 H1: β > 0
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f-2. Specify the decision rule. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)
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f-3. Find the test statistic. (Round your answer to 2 decimal places.)
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f-4. Make a decision
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Reject H0.
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Do not reject H0.
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f-5. State your conclusion.
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