For the data provided in the table below, find 90%, 95%, and 99% confidence intervals for the mean GPA. Compute the confidence intervals using the appropriate formulas and verify your results using the Excel Confidence Intervals template.
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 provided in the table below, find 90%, 95%, and 99% confidence intervals for the mean GPA. Compute the confidence intervals using the appropriate formulas and verify your results using the Excel Confidence Intervals template.
| Grade Point Averages | ||
| Gender | College | GPA |
| Female | Arts and Sciences | 2.68 |
| Male | Engineering | 2.80 |
| Male | Education | 2.92 |
| Male | Engineering | 3.00 |
| Male | Engineering | 3.01 |
| Female | Arts and Sciences | 3.13 |
| Male | Engineering | 3.14 |
| Female | Engineering | 3.17 |
| Female | Nursing | 3.20 |
| Male | Engineering | 3.20 |
| Female | Nursing | 3.20 |
| Female | Arts and Sciences | 3.21 |
| Female | Nursing | 3.25 |
| Female | Business | 3.26 |
| Female | Nursing | 3.26 |
| Female | Health Science | 3.28 |
| Female | Education | 3.29 |
| Female | Nursing | 3.34 |
| Female | Nursing | 3.36 |
| Female | Nursing | 3.40 |
| Female | Education | 3.44 |
| Female | Education | 3.45 |
| Female | Nursing | 3.48 |
| Female | Arts and Sciences | 3.50 |
| Male | Engineering | 3.51 |
| Female | Arts and Sciences | 3.61 |
| Female | Nursing | 3.67 |
| Female | Health Science | 3.70 |
| Male | Engineering | 3.72 |
| Female | Arts and Sciences | 3.72 |
| Male | Business | 3.74 |
| Male | Business | 3.75 |
| Female | Health Science | 3.76 |
| Female | Education | 3.80 |
| Male | Engineering | 3.87 |
| Female | Nursing | 3.4 |
| Female | Health Science | 3.85 |
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