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) 60 88 148 M.D. 79 80 159 Lawyer 124 88 212 Column Total 263 256 519 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 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 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? YesNo What sampling distribution will you use? normalStudent's t uniformbinomialchi-square What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. p-value > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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)	60	88	148
M.D.	79	80	159
Lawyer	124	88	212
Column Total	263	256	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 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 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?

YesNo

What sampling distribution will you use?

normalStudent's t uniformbinomialchi-square

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic.

p-value > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005

(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.

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