The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted. Personality Type Occupation Clergy (all denominations) M.D. Lawyer Column Total Row Total 64 43 107 67 95 162 52 85 137 223 Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance. 183 406 (a) What is the level of significance? State the null and alternate hypotheses. O H: Myers-Briggs preference and profession are independent H,: Myers-Briggs preference and profession are not independent. O Ho: Myers-Briggs preference and profession are not independent H,: Myers-Briggs preference and profession are independent. O H,: Myers-Briggs preference and profession are not independent H,: Myers-Briggs preference and profession are not independent. O H,: Myers-Briggs preference and profession are independent H,: Myers-Briggs preference and profession are 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? O Yes O No What sampling distribution will you use? O binomial O uniform O chi-square O student's t O normal 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? O Since the P-value > a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent. O At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.
The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted. Personality Type Occupation Clergy (all denominations) M.D. Lawyer Column Total Row Total 64 43 107 67 95 162 52 85 137 223 Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of significance. 183 406 (a) What is the level of significance? State the null and alternate hypotheses. O H: Myers-Briggs preference and profession are independent H,: Myers-Briggs preference and profession are not independent. O Ho: Myers-Briggs preference and profession are not independent H,: Myers-Briggs preference and profession are independent. O H,: Myers-Briggs preference and profession are not independent H,: Myers-Briggs preference and profession are not independent. O H,: Myers-Briggs preference and profession are independent H,: Myers-Briggs preference and profession are 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? O Yes O No What sampling distribution will you use? O binomial O uniform O chi-square O student's t O normal 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? O Since the P-value > a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent. O At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted.
Personality Type
Occupation
Clergy (all denominations)
M.D.
Lawyer
Column Total
E
I
Row Total
64
43
107
67
95
162
52
85
137
183
223
406
Use 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.
O Ho: Myers-Briggs preference and profession are independent
H,: Myers-Briggs preference and profession are not independent.
O H: Myers-Briggs preference and profession are not independent
H,: Myers-Briggs preference and profession are independent.
O Ho: Myers-Briggs preference and profession are not independent
H,: Myers-Briggs preference and profession are not independent.
O Ho: Myers-Briggs preference and profession are independent
H,: Myers-Briggs preference and profession are 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?
O Yes
O No
What sampling distribution will you use?
O binomial
O uniform
chi-square
O Student's t
O normal
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?
O Since the P-value > a, we fail to reject the null hypothesis.
O since the P-value > a, we reject the null hypothesis.
O Since the P-value s a, we reject the null hypothesis.
O Since the P-value s a, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
O At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.
O At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman