Please help me out with this statistics question. Please be as extensive as poss

Question

Please help me out with this statistics question. Please be as extensive as possible with the solution

In 1969, the National Bureau of Economic Research (NBER) conducted a survey of civilian respondents who had been in the military during World War At the time of entry into the military, volunteers had to pass a battery of aptitude tests. In the NBER study, the researchers wanted to explore the predictive ability of these aptitude tests (Aptitude) with regards to vocational success (Occupation) and if respondents educational level (Education) mediated this relationship. The following describes the different levels of each of the variables: Occupational level 01: self-employed, business A1: low E1: low 02: self-employed, professional A2 03: teacher 04: salaried, employed Aptitude Educational level A3 A4 A5: high E2 E3 E4: high

Explanation / Answer

Given table data is as below

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calculation formula for E table matrix

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expected frequecies calculated by applying E - table matrix formulae

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above

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set up null vs alternative as

null, Ho: no relation b/w education and occupational levels

alternative, H1: exists a relation b/w education and occupational levels

level of significance, = 0.05

from standard normal table, chi square value at right tailed, ^2 /2 =16.919

since our test is right tailed,reject Ho when ^2 o > 16.919

we use test statistic ^2 o = (Oi-Ei)^2/Ei

from the table , ^2 o = 1254.148

critical value

the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 4 -1 ) * ( 4 - 1 ) = 3 * 3 = 9 is 16.919

we got | ^2| =1254.148 & | ^2 | =16.919

make decision

hence value of | ^2 o | > | ^2 | and here we reject Ho

^2 p_value =0

ANSWERS

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null, Ho: no relation b/w education and occupational levels

alternative, H1: exists a relation b/w education and occupational levels

test statistic: 1254.148

critical value: 16.919

p-value:0

decision: reject Ho

exists a relation b/w education and occupational levels

MATRIX col1 col2 col3 TOTALS TOTALS row 2 239 6 1 794 1040 row 3 309 11 7 781 1108 row 3 233 70 12 922 1237 row 4 53 199 215 501 968 TOTALS 834 286 235 2998 4353

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