Lable shows the Myers-Briggs personality preferénces for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted. The Personality Type Occupation Clergy (all denominations) M.D. Lawyer Column Total E Row Total 65 42 92 83 217 107 70 162 137 406 54 189 n USE SALT 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 Hn: Myers-Briggs preference and profession are not independent H,: Myers-Briggs preference and profession are independent. O Ho: Myers-Briggs preference and profession are independent H,: Myers-Briggs preference and profession are independent. O H: Myers-Briggs preference and profession are independent H,: Myers-Briggs preference and profession are not independent. O Hn: Myers-Briggs preference and profession are not independent H,: 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? O Yes O No What sampling distribution will you use? O chi-square O normal O binomial O uniform O Student's t What are the degrees of freedom? c fe) Find or estimate the P-value of the sample test statistic
Lable shows the Myers-Briggs personality preferénces for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted. The Personality Type Occupation Clergy (all denominations) M.D. Lawyer Column Total E Row Total 65 42 92 83 217 107 70 162 137 406 54 189 n USE SALT 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 Hn: Myers-Briggs preference and profession are not independent H,: Myers-Briggs preference and profession are independent. O Ho: Myers-Briggs preference and profession are independent H,: Myers-Briggs preference and profession are independent. O H: Myers-Briggs preference and profession are independent H,: Myers-Briggs preference and profession are not independent. O Hn: Myers-Briggs preference and profession are not independent H,: 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? O Yes O No What sampling distribution will you use? O chi-square O normal O binomial O uniform O Student's t What are the degrees of freedom? c fe) Find or estimate the P-value of the sample test statistic
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:ble 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)
E
Row Total
65
42
107
M.D.
70
92
162
Lawyer
Column Total
54
83
137
189
217
406
A USE SALT
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 not independent
H: Myers-Briggs preference and profession are independent.
O Ho: Myers-Briggs preference and profession are independent
H: Myers-Briggs preference and profession are independent.
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 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?
O Yes
No
What sampling distribution will you use?
O chi-square
O normal
O binomial
O uniform
O Student'st
What are the degrees of freedom?
() Find or estimate the P-value of the sample test statistic
Transcribed Image Text:Ho: 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 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?
O Yes
O No
What sampling distribution will you use?
O chi-square
O normal
O binomial
O uniform
O Student'st
What are the degrees of freedom?
(c) Find or estimate the P-value of the sample test statistic.
O p-value > 0.100
O 0.050 < p-value < 0.100
O 0.025 < p-value < 0.050
0.010 < p-value < 0.025
O 0.005 < p-value < 0.010
O p-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?
O Since the P-value > a, we fail to reject the null hypothesis.
O Since the P-value > a, we reject the null hypothesis.
Since the P-value < a, we reject the null hypothesis.
O Since the P-value < 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.
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.
Step by step
Solved in 5 steps with 5 images
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