(Solved): he following table.shows the Myers-Briggs personality preferences for a randam sample of 406 people ...

he following table.shows the Myers-Briggs personality preferences for a randam sample of 406 people in the listed professions. E refers to ctroverted and 1 refers to introverted. e the chi-square test to determine if the listed occupations and personality preferences are independent at the \( 0.05 \) level of significance. (a) What is the level of significance? State the null and alternate hypotheses. \( H_{0} \) : Myers-Briggs preference and profession are not independent \( H_{1} \) : Myers-Briggs preference and profession are independent. \( H_{0} \) : Myers-Briggs preference and profession are independent \( H_{1} \) : Myers-Briggs preference and profession are not independent. \( H_{0} \) : Myers-Briggs preference and profession are independent \( H_{1} \) : Myers-Briggs preference and profession are independent. \( H_{0} \) : Myers-Briggs preference and profession are no: independent \( H_{1} \) : Myers-Briggs preference and profession are not 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.) Are all the expected frequencies greater than 5 ? Yes No What sampling distribution will you use? chi-square What sampling distribution will you use? chi-square uniform binomial normal Student's \( t \) What are the degrees of freedom? (c) Find or estimate the \( \rho \)-value of the sample test statistic. \( p \)-value \( >0.100 \) \[ \begin{array}{l} 0.050

\alpha \), we fail to reject the null hypothesis. Since the \( P \)-value \( >\alpha \), we reject the null hypothesis. Since the P.value \( s a \), we reject the null hypothesis. Since the P.value \( \leq a \), we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the \( 5 \% \) lovel of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent. At the \( 5 \% \) level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.