One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. After taking the test and seeing your score for this subsection, you're interested in the mean score, u, among the general population on this subsection. The website reports that u is 142, but you believe that u differs from 142. You decide to do a statistical test. You choose a random sample of people and have them take the personality test. You find that their mean score on the subsection is 148 and that the standard deviation of their scores is 22. Based on this information, answer the questions below.
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.
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