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Recall that with a normal distribution, 95% of the distribution is within 1.96 standard deviations of the mean. Using the t distribution, if you have a sample size of only 5, 95% of the area is within 2.78 standard deviations of the mean.Therefore, the standard error of the mean would be multiplied by 2.78 rather than 1.96. The values of t to be used in a confidence interval can be looked up in a table of the t distribution.he value of 1.96 is based on the fact that 95% of the area of a normal distribution is within 1.96 standard deviations of the mean; 12 is the standard error of the mean. Figure 1. The sampling distribution of the mean for N=9. The middle 95% of the distribution is shaded.
The standard deviation is a measure of spread, in this case of IQ scores. A standard devation of 15 means 68% of the norm group has scored between 85 (100 â 15) and 115 (100 + 15). In other words, 68% of the norm group has a score within one standard deviation of the average (100).