s w 2. If all the expected frequencies are not equal, then the expected frequency E can bequencies are called the observed frequencies. The frequencies obtained by calculationriT Since the frequencies for each flavor were obtained from a sample, these actual fre-these data:Section 11-1 Test for Goodness of Fit591CherryStrawberry32Orange28LimeGrape161410(as if there were no preference) are called the expected frequencies.To calculate the expected frequencies, there are two rules to follow.1. If all the expected frequencies are equal, the expected frequency E can be calculatedby using E = n/k, where n is the total number of observations and k is the numberof categories.calculated by E = n · p, where n is the total number of observations and p is theprobability for that category.avel anoigboog an expect each flavor to be selected with equal frequency. In this case, the equal frequency isbn nosmi 100/5 = 20. That is, approximately 20 people would select each flavor. A completed tableto onoupsl bo for the test is shown.Looking at the new fruit flavors example, if there were no preference, you woulds ol uliy borog tFrequencyCherryStrawberryOrangeGrapeLimeni bo in ObservedExpected32102820162014202020The observed frequencies will almost always differ from the expected frequenciesdue to sampling error; that is, the values differ from sample to sample. But the questionis: Are these differences significant (a preference exists), or are they due to chance? Thechi-square goodness-of-fit test will enable the researcher to determine the answer.Defore computing the test value, you must state the hypotheses. The null hypothesisshoul be a statement indicating that there is no difference or no change. For this exam-ple, the bypotheses are as follows:He: Consumers show no preference for flavors of the fruit soda.H: Consumers show a preference.Next, we need a measure of discrepancy between the observed values O and theexpected values E, so we use the test statistic for the chi-square goodness-of-fit test.TInteresting FactFormula for the Chi-Square Goodness-of-Fit TestE)(0Men begin to lose theirhearing more than30 years before women.The difference may bedue to males' more fre-quent exposure to suchnoisy machines aspower tools andlawnmowers.Ewith degrees of freedom equal to the number of categories minus 1, and whereO = observed frequencyE = expected frequencyNotice that the value of the test statistic is based on the difference between the observedvalues and the expected values. If the observed values are significantly different from theexpected values, then there is enough evidence to reject the null hypothesis.When there is perfect agreement between the observed and the expected values= 0. Also, ? can never be negative. Finally, the test is right-tailed becauseu. Good fir" and "Hi: Not a good fit" mean that x² will be small in the first case andlarge in the second case.d In the goodness-of-fit test, the degrees of freedom are equal to the number ec11-3 The test described shows whether or not there is a ?a.Relationshipb.PreferencePage 591DependenceС.d.None of thesethore is a ?

Name: s w 2. If all the expected frequencies are not equal, then the expect
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Description: s w 2. If all the expected frequencies are not equal, then the expected frequency E can bequencies are called the observed frequencies. The frequencies obtained by calculationriT Since the frequencies for each flavor were obtained from a sample, the

We have given chi square statistic formula for goodness of fit test and we have to select correct…

Answered: - Fact Formula for the Chi-Square…

Math

Statistics

- Fact Formula for the Chi-Square Goodne ce their an (0 - E) X = = E Momon ngual to the number of categories minus 1, and where

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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