Bluman A.G. Elementary Statistics- A Step By Step Approach

Guided Tour: Featuresand SupplementsEach chapter begins with an outlineand a list of learning objectives. Theobjectives are repeated at thebeginning of each section to helpstudents focus on the conceptspresented within that section.C H A P T E RThe NormalDistribution6592 Chapter 11 Other Chi-Square TestsObjectivesAfter completing this chapter, you should be able to1 Identify distributions as symmetric or skewed.2 Identify the properties of a normal distribution.3 Find the area under the standard normaldistribution, given various z values.4 Find probabilities for a normally distributedvariable by transforming it into a standardnormal variable.5 Find specific data values for givenpercentages, using the standard normaldistribution.OutlineIntroduction6–1 Normal Distributions6–2 Applications of the Normal Distribution6–3 The Central Limit Theorem6–4 The Normal Approximation to the BinomialDistributionSummaryStatisticsTodayStatistics and HeredityAn Austrian monk, Gregor Mendel (1822–1884), studied genetics, and his principles arethe foundation for modern genetics. Mendel used his spare time to grow a variety of peasat the monastery. One of his many experiments involved crossbreeding peas that hadsmooth yellow seeds with peas that had wrinkled green seeds. He noticed that the resultsoccurred with regularity. That is, some of the offspring had smooth yellow seeds, somehad smooth green seeds, some had wrinkled yellow seeds, and some had wrinkled greenseeds. Furthermore, after several experiments, the percentages of each type seemed toremain approximately the same. Mendel formulated his theory based on the assumptionof dominant and recessive traits and tried to predict the results. He then crossbred hispeas and examined 556 seeds over the next generation.Finally, he compared the actual results with the theoretical results to see if his theorywas correct. To do this, he used a “simple” chi-square test, which is explained in thischapter. See Statistics Today—Revisited at the end of this chapter.Source: J. Hodges, Jr., D. Krech, and R. Crutchfield, Stat Lab, An Empirical Introduction to Statistics (New York: McGraw-Hill),pp. 228–229. Used with permission.Introductionhi square distribution was used in Chapters 7 and 8 to find a confidence interval ford rd deviation and to test a hypothesis about a single variance or stanfrequencydistributions, such as “If a samplel ach color be selected with thehe independence oOver 300 examples with detailed solutionsserve as models to help students solveproblems on their own. Examples are solvedby using a step by step explanation, andillustrations provide a clear display of resultsfor students.The outline and learning objectives are followed by afeature titled Statistics Today, in which a real-lifeproblem shows students the relevance of thematerial in the chapter. This problem is subsequentlysolved near the end of the chapter by using thestatistical techniques presented in the chapter.38 Chapter 2 Frequency Distributions and GraphsTwo types of frequency distributions that are most often used are the categoricalfrequency distribution and the grouped frequency distribution. The procedures for constructingthese distributions are shown now.Categorical Frequency DistributionsThe categorical frequency distribution is used for data that can be placed in specific categories,such as nominal- or ordinal-level data. For example, data such as political affiliation,religious affiliation, or major field of study would use categorical frequency distributions.Example 2–1 Distribution of Blood TypesTwenty-five army inductees were given a blood test to determine their blood type. Thedata set isA B B AB OO O B AB BB B O A OA O O O ABAB A O B AConstruct a frequency distribution for the data.SolutionSince the data are categorical, discrete classes can be used. There are four blood types:A, B, O, and AB. These types will be used as the classes for the distribution.The procedure for constructing a frequency distribution for categorical data isgiven next.Step 1 Make a table as shown.A B C DClass Tally Frequency PercentABOABStep 2 Tally the data and place the results in column B.Step 3 Count the tallies and place the results in column C.Step 4 Find the percentage of values in each l% fxv