The results of a common standardized test used in psychology research is designed so that the population mean is 155 and the standard deviation is 10. A subject earns a score of 165 . What is the \( z \)-score for this raw score? \( z \)-score \( = \)

To find the \( z \)-score for a raw score of 165, you can use the formula: \[ z = \frac{(X - \mu)}{\sigma} \] Where \( X \) is the raw score, \( \mu \) is the population mean, and \( \sigma \) is the standard deviation. Plugging in the values: \[ z = \frac{(165 - 155)}{10} = \frac{10}{10} = 1 \] So, the \( z \)-score for the raw score of 165 is 1. Now, let’s dive into the fascinating world of standardized testing! Using standardized tests, psychologists can compare an individual’s performance to a broader population, allowing for a clearer understanding of where they stand. Whether it's academic achievement, personality traits, or cognitive abilities, these tests provide a snapshot of a person’s capabilities in relation to others. Speaking of interpretation, a common pitfall is misinterpreting the \( z \)-score. A \( z \)-score of 1 means the score is 1 standard deviation above the mean, but some might mistakenly think it reflects a percentage or rank directly. Always remember: the \( z \)-score indicates how far and in which direction (above or below the mean) a raw score lies!