The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing. Myers-Briggs Arts & Science Allied Health Row Total Preference Business 9 40 IN 66 21 96 154 EN 82 32 IS 60 39 16 115 ES 70 40 44 154 Column Total 278 128 113 519 LAUSE SALT Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: Myers-Briggs type and area of study are independent. H₁: Myers-Briggs type and area of study are not independent. OH: Myers-Briggs type and area of study are independent. H₁: Myers-Briggs type and area of study are independent. OH: Myers-Briggs type and area of study are not independent. H₁: Myers-Briggs type and area of study are independent. OH: Myers-Briggs type and area of study are not independent. H₁: Myers-Briggs type and area of study 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 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.) O p-value> 0.100 O 0.050 < p-value < 0.100 O 0.025 a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value sa, 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 sufficient evidence to conclude that Myers-Briggs type and area of study are not independent. O At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs type and area of study are not independent. 7

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

Q4. Please Help

The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing.
Myers-Briggs Arts & Science
Business Allied Health
Row Total
Preference
IN
66
21
9
40
96
154
EN
82
32
IS
60
39
16
115
ES
70
40
44
154
Column Total
278
128
113
519
LAUSE SALT
Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance.
(a) What is the level of significance?
State the null and alternate hypotheses.
OH: Myers-Briggs type and area of study are independent.
H₁: Myers-Briggs type and area of study are not independent.
OH: Myers-Briggs type and area of study are independent.
H₁: Myers-Briggs type and area of study are independent.
O Ho: Myers-Briggs type and area of study are not independent.
H₁: Myers-Briggs type and area of study are independent.
OH: Myers-Briggs type and area of study are not independent.
H₁: Myers-Briggs type and area of study 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 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.)
O p-value > 0.100
O 0.050 < p-value < 0.100
O 0.025 < p-value < 0.050
O 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.
O Since the P-value sa, we reject the null hypothesis.
O Since the P-value sa, 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 sufficient evidence to conclude that Myers-Briggs type and area of study are not independent.
O At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs type and area of study are not independent.
Transcribed Image Text:The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing. Myers-Briggs Arts & Science Business Allied Health Row Total Preference IN 66 21 9 40 96 154 EN 82 32 IS 60 39 16 115 ES 70 40 44 154 Column Total 278 128 113 519 LAUSE SALT Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance. (a) What is the level of significance? State the null and alternate hypotheses. OH: Myers-Briggs type and area of study are independent. H₁: Myers-Briggs type and area of study are not independent. OH: Myers-Briggs type and area of study are independent. H₁: Myers-Briggs type and area of study are independent. O Ho: Myers-Briggs type and area of study are not independent. H₁: Myers-Briggs type and area of study are independent. OH: Myers-Briggs type and area of study are not independent. H₁: Myers-Briggs type and area of study 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 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.) O p-value > 0.100 O 0.050 < p-value < 0.100 O 0.025 < p-value < 0.050 O 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. O Since the P-value sa, we reject the null hypothesis. O Since the P-value sa, 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 sufficient evidence to conclude that Myers-Briggs type and area of study are not independent. O At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs type and area of study are not independent.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
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