Applied Statistical Designs for the Researcher by Daryl S. Paulson

By Daryl S. Paulson

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An important, special case of the normal distribution is the standard normal distribution, where m ¼ 0 and s2 ¼ 1. The statistic is converted to this scale for use of the normal distribution tables A and B. In this case, the random variable, Z ¼ ðX À mÞ=s, follows the standard normal distribution, Z $ N ð0; 1Þ. This equation transforms any normal random variable, X, into a standard normal random variable, Z, that can then be used in a table of the cumulative standard normal distribution. A statistical population is the set of all elements under observation.

32 Chapter 2 FIGURE 6 Various confidence levels. , for a ¼ 0:20, 1 À a ¼ 0:80 or 80%; for a ¼ 0:05, 1À a ¼ 0:95 or 95%; for a ¼ 0:01, 1 À a ¼ 0:99 or 99%). Recall that the con¢dence level is set, not calculated by the experimenter. The most commonly used con¢dence level in science is 95%. If the experimenter desires a greater degree of con¢dence, the CI width increases (Fig. 6). S. males 25 years of age, the point estimate may be 175 pounds and the interval estimate 175 Æ 5, or (170, 180), pounds at 80% con¢dence.

The median is found in the stem ^leaf column and is the midvalue. There is an interesting pattern at stem ‘‘8,’’ subtly suggesting that the data are bimodal (two peaks). Again, there are not enough data to tell. So FIGURE 1 Stem-and-leaf display.

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