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, Myers-Briggs Preference Arts & Science Business Allied Health Row Total IN 60 27 96 EN 87 38 29 154 IS 54 37 24 115 ES 80 39 35 154 Column Total 281 123 115 519 A USE 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 Hg: Myers-Briggs type and area of study are not independent. H: Myers-Briggs type and area of study are not independent. OH: Myers-Briggs type and area of study are independent. H: Myers-Briggs type and area of study are independent. O Hg: Myers-Briggs type and area of study are not independent. H: Myers-Briggs type and area of study are independent. OH: Myers-Briggs type and area of study are independent. H,: 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 frequendes greater than 5? O Yes O No
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, Myers-Briggs Preference Arts & Science Business Allied Health Row Total IN 60 27 96 EN 87 38 29 154 IS 54 37 24 115 ES 80 39 35 154 Column Total 281 123 115 519 A USE 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 Hg: Myers-Briggs type and area of study are not independent. H: Myers-Briggs type and area of study are not independent. OH: Myers-Briggs type and area of study are independent. H: Myers-Briggs type and area of study are independent. O Hg: Myers-Briggs type and area of study are not independent. H: Myers-Briggs type and area of study are independent. OH: Myers-Briggs type and area of study are independent. H,: 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 frequendes greater than 5? O Yes O No
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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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
Preference
Arts & Science
Business
Allied Health
Row Total
IN
60
27
96
EN
87
38
29
154
54
37
24
115
ES
80
39
35
154
Column Total
281
123
115
519
A USE 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 H: Myers-Briggs type and area of study are not independent.
H: Myers-Briggs type and area of study are not independent.
OH: Myers-Briggs type and area of study are independent.
H: Myers-Briggs type and area of study are independent.
O H: Myers-Briggs type and area of study are not independent.
H,: Myers-Briggs type and area of study are independent.
OH: Myers-Briggs type and area of study are independent.
H: 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 frequendies greater than 5?
O Yes
O No
What sampling distribution will you use?
O normal
O chi-square
O binomial
O uniform
O Student's t
What are the degrees of freedom?
(c) Find or estimate the Pvalue of the sample test statistic. (Round your answer to three decimal places.)
O pvalue > 0.100
O 0.050 < pvalue < 0.100
O 0.025 < p-value < 0.050
O 0.010 < p-value < 0.025
O 0.005 < p-value < 0.010
O prvalue < 0.00s
(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 nul hypothesis.
O Since the P.value sa, we reject the null hypothesis.
O Since the P-value sa, we fal to reject the null hypothesis.
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