The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the

Question:

The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions (Myers-Briggs Type Indicator Atlas of Type Tables, by Macdaid, McCaulley, and Kainz). E refers to extroverted and I refers to introverted.

Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance.
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)€“(c), will you reject or fail to reject the null hypothesis of independence?
(e) Your conclusion in the context of the application.
Use the expected values E to the hundredths place.

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