266 CHAPTER 6 Normal Probability Distributions Significance In Chapter 4 we saw that probabilities can be used to determine whether values are significantly high or significantly low. Chapter 4 referred to x successes among n trials, but we can adapt those criteria to apply to continuous variables as follows: Significantly high: The value x is significantly high if P(x or greater) … 0.05.* Significantly low: The value x is significantly low if P(x or less) … 0.05.* *The value of 0.05 is not absolutely rigid, and other values such as 0.01 could be used instead. Significantly Low Birth Weights EXAMPLE 4 Use the preceding criteria to identify significantly low birth weights (grams) of males based on Data Set 6 “Births” in Appendix B. Assume that males have normally distributed birth weights with a mean of 3272.8 g and a standard deviation of 660.2 g. YOUR TURN. Do Exercise 23 “Significance.” SOLUTION Step 1: We begin with the graph shown in Figure 6-15. We have entered the mean of 3272.8 and we have identified the x value separating the lowest 5% of male birth weights. x 5 ? 0.05 m 5 3272.8 FIGURE 6-15 Male Birth Weights Step 2: Technology: To use technology, refer to the instructions at the end of this section. Technology will show that the value of x in Figure 6-15 is 2186.9 g. Table A-2: If using Table A-2, we must work with cumulative areas from the left. For the value of x, the cumulative area from the left is 0.05, so search for an area of 0.05 in the body of the table to get z = -1.645 (identified by the asterisk between 0.0505 and 0.0495). Having found the z score, we now proceed to convert it to a birth weight. Step 3: We now solve for x by using Formula 6-2 directly or by using the following version of Formula 6-2: Value of x: x = m + 1z # s2 = 3272.8 + 1-1.645 # 660.22 = 2186.8 g Step 4: Referring to Figure 6-15, we see that the value of x = 2186.9 g (or 2186.8 g if using Table A-2) is reasonable because it is less than the mean of 3272.8 g. INTERPRETATION The birth weight of 2186.9 g is on the borderline that separates significantly low male birth weights from male birth weights that are not significantly low. (The World Health Organization uses 2500 g as the cutoff for low birth weights of males and females.) Babies with low birth weights are often given special treatments, such as care in the Neonatal Intensive Care Unit or the use of a temperature-controlled bed.
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