210 CHAPTER 5 Discrete Probability Distributions Identifying Significant Results with the Range Rule of Thumb The following range rule of thumb (from Section 3-2) is based on the principle that the vast majority of values should lie within 2 standard deviations of the mean. Range Rule of Thumb for Identifying Significant Values Significantly low values are 1m - 2s2 or lower. Significantly high values are m + 2s or higher. Values not significant: Between 1m - 2s2 and 1m + 2s2 Figure 5-3 (repeated from Figure 3-4 in Section 3-2) illustrates the above criteria: Values not significant Significantly low values Significantly high values m m − 2s m + 2s FIGURE 5-3 Range Rule of Thumb for Identifying Significant Values CAUTION Know that the use of the number 2 in the range rule of thumb is somewhat arbitrary, and this is a guideline, not an absolutely rigid rule. Identifying Significant Results with the Range Rule of Thumb EXAMPLE 4 In Example 3 we found that for two births, the mean number of females is m = 1.0 female and the standard deviation is s = 0.7 female. Use those results and the range rule of thumb to determine if 2 females in 2 births is significantly high. Using the range rule of thumb, the outcome of 2 females is significantly high if it is greater than or equal to m + 2s. With m = 1.0 female and s = 0.7 female, we get m + 2s = 1 + 210.72 = 2.4 females Significantly high numbers of females are 2.4 and above. SOLUTION YOUR TURN. Do Exercise 17 “Range Rule of Thumb for Significant Events.” Based on these results, we conclude that 2 females is not a significantly high number of females (because 2 is not greater than or equal to 2.4). INTERPRETATION Identifying Significant Results with Probabilities: ■ Significantly high number of successes: x successes among n trials is a significantly high number of successes if the probability of x or more successes is 0.05 or less. That is, x is a significantly high number of successes if P(x or more) … 0.05.* ■ Significantly low number of successes: x successes among n trials is a significantly low number of successes if the probability of x or fewer successes is 0.05 or less. That is, x is a significantly low number of successes if P(x or fewer) … 0.05.* *The value 0.05 is not absolutely rigid. Other values, such as 0.01, could be used to distinguish between results that are significant and those that are not significant.
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