Chapter 7, Section 2, Exercise 031 Find the expected count and the contribution

Question

Chapter 7, Section 2, Exercise 031 Find the expected count and the contribution to the chi-square statistic for the left-parenthesis B comma E right-parenthesis cell in the two-way table below.

Round your answer for the excepted count to one decimal place, and your answer for the contribution to the chi-square statistic to three decimal places.

Expected count =...

contribution to the chi-square statistic=...

D E F G Total A 38 32 41 37 148 B 78 86 67 54 285 C 19 35 27 31 112 Total 135 153 135 122 545

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 X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 = 12.59
since our test is right tailed,reject Ho when ^2 o > 12.59
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 10.705
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 4 - 1 ) = 2 * 3 = 6 is 12.59
we got | ^2| =10.705 & | ^2 | =12.59
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0.005
ANSWERS
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null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
test statistic: 10.10.705
critical value: 12.59
p-value:0.005
decision: do not reject Ho              

A 38 32 41 37 148 A1 B 78 86 67 54 285 A2 C 19 35 27 31 112 A3 Totals 135 153 135 122 545 B1 B2 B3 B4

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