A sample that does not provide a good representation of the population from which it was collected is referred to as a(n) biased sample.
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Step 1: A biased sample is a sample that does not accurately represent the population from which it was collected. Show more…
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$\mathrm{A}(\mathrm{n})$___ sample is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups.
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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 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 $\mathrm{F}$ refers to feeling. $$ \begin{array}{l|c|c|c} \hline & \multicolumn{2}{c} {\text { Personality Preference Type }} & \\ \cline { 2 - 3 } \text { Occupation } & \multicolumn{1}{c} {\text { T }} & \text { Row Total } \\ \hline \text { Clergy (all denominations) } & 57 & 91 & 148 \\ \hline \text { M.D. } & 77 & 82 & 159 \\ \hline \text { Lawyer } & 118 & 94 & 212 \\ \hline \text { Column Total } & 252 & 267 & 519 \\ \hline \end{array} $$ Use the chi-square test to determine if the listed occupations and personality preferences are independent at the $0.01$ level of significance.
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