A public opinion poll surveyed a simple random sample of 1500 city residents. Th
ID: 3320812 • Letter: A
Question
A public opinion poll surveyed a simple random sample of 1500 city residents. The residents were classified by gender, so either male or female, along with religion. (Catholic, Christian, or Other)
Religion
Row Total
Catholic
Christian
Other
Male
335
210
170
400
Female
330
300
155
600
Total
665
510
325
1000
Is there a gender gap?
Do the men's religion differ significantly from the women's religion? Use a 0.05 level of significance.
Religion
Row Total
Catholic
Christian
Other
Male
335
210
170
400
Female
330
300
155
600
Total
665
510
325
1000
Explanation / Answer
the men's religion differ significantly from the women's religion
Given table data is as below MATRIX col1 col2 col3 TOTALS row 1 335 210 170 715 row 2 330 300 155 785 TOTALS 665 510 325 N = 1500 ------------------------------------------------------------------calculation formula for E table matrix E-TABLE col1 col2 col3 row 1 row1*col1/N row1*col2/N row1*col3/N row 2 row2*col1/N row2*col2/N row2*col3/N ------------------------------------------------------------------
expected frequecies calculated by applying E - table matrix formulae E-TABLE col1 col2 col3 row 1 316.983 243.1 154.917 row 2 348.017 266.9 170.083 ------------------------------------------------------------------
calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 335 316.983 18.017 324.612 1.024 210 243.1 -33.1 1095.61 4.507 170 154.917 15.083 227.497 1.469 330 348.017 -18.017 324.612 0.933 300 266.9 33.1 1095.61 4.105 155 170.083 -15.083 227.497 1.338 ^2 o = 13.376 ------------------------------------------------------------------
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 = 13.376
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| =13.376 & | ^2 | =5.991
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0.001
ANSWERS
---------------
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: 13.376
critical value: 5.991
p-value:0.001
decision: reject Ho
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