6. Is there a relationship between income category and the fraction of families

Question

6. Is there a relationship between income category and the fraction of families with more than two children? Use the following data: Number of Salary under Salary between Children Two or less More than 2 68 total Salary over $25,000 total S $10,000 $10,000-$25,000 13 28 41 21 9 30 45 105 150 79 Is there a relationship between income category and the fraction of families with more than two children? State the null and alternative hypothesis. State the observed values 14points State the expected values Give a conclusion 4 points 4 points 4 points

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 income category and the fraction of families

alternative, H1: exists a relation b/w income category and the fraction of families

level of significance, = 0.05

from standard normal table, chi square value at right tailed, ^2 /2 =5.991

since our test is right tailed,reject Ho when ^2 o > 5.991

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

from the table , ^2 o = 32.636

critical value

the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 3 - 1 ) = 1 * 2 = 2 is 5.991

we got | ^2| =32.636 & | ^2 | =5.991

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 income category and the fraction of families

alternative, H1: exists a relation b/w income category and the fraction of families

test statistic: 32.636

critical value: 5.991

p-value:0

decision: reject Ho

MATRIX col1 col2 col3 TOTALS row 1 11 13 21 45 row 2 68 28 9 105 TOTALS 79 41 30 N = 150

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