The following table shows the Myers-Briggs personality preferences for a random sample of 519 people in the listed professions. T refers to thinking and \( \mathrm{F} \) refers to feeling. \begin{tabular}{|l|c|c|c|} \hline \multirow{2}{*}{ Occupation } & \multicolumn{2}{c|}{ Personality Type } & \multirow{2}{*}{ Row Total } \\ \cline { 2 - 3 } & T & F & 148 \\ \hline Clergy (all denominations) & 55 & 93 & 159 \\ \hline M.D. & 81 & 78 & 212 \\ \hline Lawyer & 116 & 96 & 519 \\ \hline Column Total & 252 & 267 & 5 \\ \hline \end{tabular} ? USE SALT Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 level of significance. (a) What is the level of significance? \( \square \) State the null and alternate hypotheses. \( \mathrm{H}_{0} \) : Myers-Briggs preference and profession are independent. \( H_{1} \) : Myers-Briggs preference and profession are not independent. \( \mathrm{H}_{0} \) : Myers-Briggs preference and profession are not independent. \( \mathrm{H}_{1} \) : Myers-Briggs preference and profession are independent. \( \mathrm{H}_{0} \) : Myers-Briggs preference and profession are not independent. \( \mathrm{H}_{1} \) : Myers-Briggs preference and profession are not independent. \( \mathrm{H}_{0}: \) Myers-Briggs preference and profession are independent.
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The following table shows the Myers-Briggs personality preferences for a random sample of 519 people in the listed professions (Atlas of Type Tables by Macdaid, McCaulley, and Kainz). T refers to thinking and F refers to feeling. $$\begin{array}{l|c|c|c} \hline \multirow{2}{*} {\text { Occupation }} & \multicolumn{2}{c} {\text { Personality Preference Type }} \\ \)\cline { 2 - 5 } & \( \mathrm{T} & \mathrm{F} & \text { Row Total } \\ \hline \text { Clergy (all denominations) } & 57 & 91 & 148 \\ \hline \text { M.D. } & 77 & 82 & 159 \\ \hline \text { Lawyer } & 118 & 94 & 212 \\ \hline \text { Column Total } & 252 & 267 & 519 \\ \hline \end{array}$$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 level of significance.
Chi-Square and F Distributions
Chi-Square: Tests of Independence and of Homogeneity
The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing. Myers-Briggs Preference | Arts & Science | Business | Allied Health | Row Total IN | 68 | 17 | 11 | 96 EN | 87 | 40 | 27 | 154 IS | 52 | 38 | 25 | 115 ES | 70 | 44 | 40 | 154 Column Total | 277 | 139 | 103 | 519 Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance. (a) What is the level of significance? 0.05 State the null and alternate hypotheses. - H0: Myers-Briggs type and area of study are independent. - H1: Myers-Briggs type and area of study are not independent. - H0: Myers-Briggs type and area of study are not independent. - H1: Myers-Briggs type and area of study are not independent. - H0: Myers-Briggs type and area of study are not independent. - H1: Myers-Briggs type and area of study are independent. - H0: Myers-Briggs type and area of study are independent. - H1: Myers-Briggs type and area of study are independent. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
Sri K.
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. Psychology: Myers-Briggs The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students (Applications of the Myers-Briggs Type Indicator in Higher Education, edited by Provost and Anchors). In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing. $$ \begin{array}{l|c|c|c|c} \hline \begin{array}{l} \text { Myers-Briggs } \\ \text { Preference } \end{array} & \begin{array}{c} \text { Arts \& } \\ \text { Science } \end{array} & \multicolumn{1}{c} {\text { Business }} & \multicolumn{1}{c} {\begin{array}{c} \text { Allied } \\ \text { Health } \end{array}} & \text { Row Total } \\ \hline \text { IN } & 64 & 15 & 17 & 96 \\ \hline \text { EN } & 82 & 42 & 30 & 154 \\ \hline \text { IS } & 68 & 35 & 12 & 115 \\ \hline \text { ES } & 75 & 42 & 37 & 154 \\ \hline \text { Column Total } & 289 & 134 & 96 & 519 \\ \hline \end{array} $$ Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the $0.05$ level of significance.
Chi-Square and $F$ Distributions
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