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) 58 90 148 M.D. 72 87 159 Lawyer 119 93 212 Column Total 249 270 519   (a) State the null and alternate hypotheses. 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.     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 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.) (c) What sampling distribution will you use? binomial uniform     chi-square normal Student's t (d) Find or estimate the P-value of the sample test statistic. p-value > 0.100 0.050 < p-value < 0.100     0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005 (e) 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 > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis.     Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis. (f) 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.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
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) 58 90 148
M.D. 72 87 159
Lawyer 119 93 212
Column Total 249 270 519
 
(a) State the null and alternate hypotheses.
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.    
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 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.)

(c) What sampling distribution will you use?
binomial
uniform    
chi-square
normal
Student's t

(d) Find or estimate the P-value of the sample test statistic.
p-value > 0.100
0.050 < p-value < 0.100    
0.025 < p-value < 0.050
0.010 < p-value < 0.025
0.005 < p-value < 0.010
p-value < 0.005

(e) 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 > α, we fail to reject the null hypothesis.
Since the P-value > α, we reject the null hypothesis.    
Since the P-value ≤ α, we reject the null hypothesis.
Since the P-value ≤ α, we fail to reject the null hypothesis.

(f) 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.  
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Knowledge Booster
Chi-squared Tests
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.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman