Question

In: Statistics and Probability

The following table shows the Myers-Briggs personality preference and area of study for a random sample...

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 64 17 15 96
EN 84 44 26 154
IS 53 30 32 115
ES 70 44 40 154
Column Total 271 135 113 519

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.

H0: Myers-Briggs type and area of study are not independent.
H1: Myers-Briggs type and area of study are not independent.H0: Myers-Briggs type and area of study are not independent.
H1: Myers-Briggs type and area of study are independent.    H0: Myers-Briggs type and area of study are independent.
H1: Myers-Briggs type and area of study are not independent.H0: Myers-Briggs type and area of study are independent.
H1: Myers-Briggs type and area of study 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?

YesNo    


What sampling distribution will you use?

Student's tbinomial    uniformchi-squarenormal


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.)

p-value > 0.1000.050 < p-value < 0.100    0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-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?

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.


(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs type and area of study are not independent.At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs type and area of study are not independent.  

Solutions

Expert Solution

a)

level of significance =0.05

H0: Myers-Briggs type and area of study are independent.
H1: Myers-Briggs type and area of study are not independent

b)

applying chi square test:

Expected Ei=row total*column total/grand total Arts Business Allied Total
IN 50.127 24.971 20.902 96
EN 80.412 40.058 33.530 154
IS 60.048 29.913 25.039 115
ES 80.412 40.058 33.530 154
total 271 135 113 519
chi square    χ2 =(Oi-Ei)2/Ei Arts Business Allied Total
IN 3.8393 2.5445 1.6664 8.0502
EN 0.1601 0.3880 1.6910 2.2390
IS 0.8273 0.0003 1.9355 2.7630
ES 1.3483 0.3880 1.2485 2.9847
total 6.1750 3.3207 6.5414 16.037
value of the chi-square statistic =16.037
Are all the expected frequencies greater than 5? :Yes
What sampling distribution will you use? chi-square
degrees of freedom =(row-1)*(column-1)=6

c)

0.010 < p-value < 0.025

d)

Since the P-value ≤ α, we reject the null hypothesis.

e)

At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs type and area of study are not independen


Related Solutions

The following table shows the Myers-Briggs personality preference and area of study for a random sample...
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 59 8 29 96 EN 87 47 20 154 IS 59 36 20 115 ES 71 44 39 154 Column Total 276 135 108 519...
The following table shows the Myers-Briggs personality preference and area of study for a random sample...
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 62 16 18 96 EN 86 38 30 154 IS 62 40 13 115 ES 71 39 44 154 Column Total 281 133 105 519...
The following table shows the Myers-Briggs personality preference and area of study for a random sample...
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 63 10 23 96 EN 84 42 28 154 IS 54 31 30 115 ES 77 42 35 154 Column Total 278 125 116 519...
The following table shows the Myers-Briggs personality preference and area of study for a random sample...
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 59 10 27 96 EN 85 41 28 154 IS 61 34 20 115 ES 75 43 36 154 Column Total 280 128 111 519...
The following table shows the Myers-Briggs personality preference and area of study for a random sample...
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 68 17 11 96 EN 79 45 30 154 IS 54 37 24 115 ES 76 40 38 154 Column Total 277 139 103 519...
The following table shows the Myers-Briggs personality preference and area of study for a random sample...
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 68 10 18 96 EN 77 40 37 154 IS 54 31 30 115 ES 71 44 39 154 Column Total 270 125 124 519...
The following table shows the Myers-Briggs personality preference and area of study for a random sample...
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 64 8 24 96 EN 77 38 39 154 IS 60 37 18 115 ES 76 45 33 154 Column Total 277 128 114 519...
The following table shows the Myers-Briggs personality preference and area of study for a random sample...
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 63 11 22 96 EN 82 47 25 154 IS 60 40 15 115 ES 74 38 42 154 Column Total 279 136 104 519...
The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in...
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 E I Row Total Clergy (all denominations) 66 41 107 M.D. 73 89 162 Lawyer 52 85 137 Column Total 191 215 406 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...
The following table shows the Myers-Briggs personality preferences for a random sample of 406 people in...
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 E I Row Total Clergy (all denominations) 64 43 107 M.D. 63 99 162 Lawyer 54 83 137 Column Total 181 225 406 (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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT