Section 10.1 Chi-Square: Tests of Independence and of Homogeneity 637 For Problems 9–19, please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. (b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? What sampling distribution will you use? What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? (e) Interpret your conclusion in the context of the application. Use the expected values E to the hundredths place. 9.| Psychology: Myers-Briggs The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed pro- fessions (Atlas of Type Tables by Macdaid, McCaulley, and Kainz). E refers to extroverted and I refers to introverted. Personality Preference Type Occupation E Row Total Clergy (all denominations) 62 45 107 М.D. 68 94 162 Lawyer 56 81 137 Column Total 186 220 406 Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance.

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.