The following table shows the Myers-Briggs personality preferences for a random

Question

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 F refers to feeling. Personality Type Occupation T F Row Total Clergy (all denominations) 59 89 148 M.D. 82 77 159 Lawyer 121 91 212 Column Total 262 257 519 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? State the null and alternate hypotheses. H0: Myers-Briggs preference and profession are not independent. H1: Myers-Briggs preference and profession are not independent. H0: Myers-Briggs preference and profession are independent. H1: Myers-Briggs preference and profession are independent. H0: Myers-Briggs preference and profession are not independent. H1: Myers-Briggs preference and profession are independent. H0: Myers-Briggs preference and profession are independent. H1: 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? uniform chi-square binomial normal Student's t What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? Since the P-value > , we fail to reject the null hypothesis. Since the P-value > , we reject the null hypothesis. Since the P-value , we reject the null hypothesis. Since the P-value , we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 1% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent. At the 1% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

Explanation / Answer

The statistical software output for this problem is:

Contingency table results:
Rows: Occupation
Columns: None

Chi-Square test:

Hence,

a) Level of significance = 0.01

Hypotheses:

H0: Myers-Briggs preference and profession are independent.

H1: Myers-Briggs preference and profession are not independent.

b) Chi - square = 4.231

Yes

Chi - square

Degrees of freedom = 1

c) P - value = 0.040

d) Since the P-value > , we fail to reject the null hypothesis.

e) At the 1% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.