For the data in the Excel file Education and Income, find 95% confidence intervals for the mean annual income of males and the mean annual income of females. Can you conclude that the mean income of one group is larger than the other? Education and Income Gender Age Level of Education Gross Annual Income Female 40-60 Graduate Degree $75,000 Female 25-39 Bachelor's Degree $47,000 Male 40-60 High School/GED $40,000 Female 25-39 Some College $30,000 Female 25-39 Some College $60,000 Female 40-60 Bachelor's Degree $80,000 Female 25-39 Bachelor's Degree $10,000 Female 25-39 Bachelor's Degree $43,000 Male 25-39 Bachelor's Degree $130,000 Female 40-60 Bachelor's Degree $89,000 Female 40-60 Graduate Degree $50,000 Female 18-24 Some College $13,462 Female 25-39 Bachelor's Degree $85,000 Male 25-39 Bachelor's Degree $60,000 Male 40-60 Graduate Degree $200,000 Female 25-39 Associates Degree $44,000 Male 25-39 High School/GED $26,000 Male 25-39 Some College $46,100 Male 25-39 Graduate Degree $15,000 Female 25-39 Some College $15,288 Male 25-39 Bachelor's Degree $58,000 Female 18-24 Bachelor's Degree $10,000 Female 25-39 Bachelor's Degree $85,000 Male 18-24 Bachelor's Degree $20,000
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.
For the data in the Excel file Education and Income, find 95% confidence intervals for the mean annual income of males and the mean annual income of females. Can you conclude that the mean income of one group is larger than the other?
| Education and Income | |||
| Gender | Age | Level of Education | Gross Annual Income |
| Female | 40-60 | Graduate Degree | $75,000 |
| Female | 25-39 | Bachelor's Degree | $47,000 |
| Male | 40-60 | High School/GED | $40,000 |
| Female | 25-39 | Some College | $30,000 |
| Female | 25-39 | Some College | $60,000 |
| Female | 40-60 | Bachelor's Degree | $80,000 |
| Female | 25-39 | Bachelor's Degree | $10,000 |
| Female | 25-39 | Bachelor's Degree | $43,000 |
| Male | 25-39 | Bachelor's Degree | $130,000 |
| Female | 40-60 | Bachelor's Degree | $89,000 |
| Female | 40-60 | Graduate Degree | $50,000 |
| Female | 18-24 | Some College | $13,462 |
| Female | 25-39 | Bachelor's Degree | $85,000 |
| Male | 25-39 | Bachelor's Degree | $60,000 |
| Male | 40-60 | Graduate Degree | $200,000 |
| Female | 25-39 | Associates Degree | $44,000 |
| Male | 25-39 | High School/GED | $26,000 |
| Male | 25-39 | Some College | $46,100 |
| Male | 25-39 | Graduate Degree | $15,000 |
| Female | 25-39 | Some College | $15,288 |
| Male | 25-39 | Bachelor's Degree | $58,000 |
| Female | 18-24 | Bachelor's Degree | $10,000 |
| Female | 25-39 | Bachelor's Degree | $85,000 |
| Male | 18-24 | Bachelor's Degree | $20,000 |
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