![]() In the Standard Normal Distribution, the mean is always equal to 0 and the. a sample mean) has a normal distribution. A Z score is a number of standard deviations a score is above or below the mean. In a z-test, we assume that under the null hypothesis, the test statistic of interest (e.g. You may be getting mixed up with a z-test. Since \(x = 17\) and \(y = 4\) are each two standard deviations to the right of their means, they represent the same, standardized weight gain relative to their means. The z-score represents the number of standard deviations that a data is from the mean. A negative weight gain would be a weight loss. To understand the concept, suppose \(X \sim N(5, 6)\) represents weight gains for one group of people who are trying to gain weight in a six week period and \(Y \sim N(2, 1)\) measures the same weight gain for a second group of people. The z-score allows us to compare data that are scaled differently. Therefore, \(x = 17\) and \(y = 4\) are both two (of their own) standard deviations to the right of their respective means. Column A represents this z score, Column B represents the distance between the mean of the standard. This means that four is \(z = 2\) standard deviations to the right of the mean. The raw scores must first be transformed into a z score.
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