Chapter 7, Section 2, Exercise 030 Find the expected count and the contribution
ID: 3224164 • Letter: C
Question
Chapter 7, Section 2, Exercise 030 Find the expected count and the contribution to the chi-square statistic for the (Group 1, Yes) 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 = ...
yes No Total Group 1 56 44 100 Group 2 140 68 208 Group 3 66 24 90 Total 262 136 398Explanation / 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 =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 = 6.75
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 2 - 1 ) = 2 * 1 = 2 is 5.991
we got | ^2| =6.75 & | ^2 | =5.991
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0.034
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: 6.75
critical value: 5.991
p-value:0.034
decision: reject Ho