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  3. the following table shows the myers-briggs persona

The following table shows the Myers-Briggs personality preferences for a random sample of 400 people in the...

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Basic Math

The following tableshows the Myers-Briggs personality preferences for a random sampleof 400 people in the listed professions.

Occupation

Extroverted

Introverted

Row Total

Clergy (alldenominations)

60

44

104

M.D.

70

91

161

Lawyer

54

81

135

Column Total

184

216

400

Use the chi-squaretest to determine if the listed occupations and personalitypreferences are independent at the 0.01 level of significance.Find(or estimate) the P-value of the sample test statistic.

Answer & Explanation Solved by verified expert
4.0 Ratings (595 Votes)

Null hypotheisis:Ho:   listed occupations and personality preferences are independent.
alternate hypothesis:Ha: listed occupations and personality preferences are dependent.
degree of freedom(df) =(rows-1)*(columns-1)=
for 2 df and 0.01 level of signifcance critical region       ?2=
Applying chi square test of independence:
Expected Ei=row total*column total/grand total Extroverted Introverted Total
Clergy 47.84 56.16 104
MD 74.06 86.94 161
Lawyer 62.10 72.90 135
total 184 216 400
chi square    ?2 =(Oi-Ei)2/Ei Extroverted Introverted Total
Clergy 3.0908 2.6329 5.7238
MD 0.2226 0.1896 0.4122
Lawyer 1.0565 0.9000 1.9565
total 4.3699 3.7225 8.0925
test statistic X2 = 8.092
p value = 0.0175
since test statistic does not falls in rejection region we fail to reject null hypothesis
we do not have have sufficient evidence to conclude that, listed occupations and personality preferences are dependent

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