Consider the following situation: In a study of the relationship between health
ID: 3337702 • Letter: C
Question
Consider the following situation: In a study of the relationship between health risk and income, researchers asked a large group of people living in Massachusetts a series of questions. Some of their results appear below. Income Low Medium High total Smoke 634 332 247 1213 Don't Smoke 1846 1622 1868 5336 total 2480 1954 2115 6549 A. Define all necessary stochastic variables, one per line. If you do not need the line, enter "NA" B. Describe a stochastic process that you would use to generate the data sequence necessary to test your hypothesis.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
E-TABLE
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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 = 150.176
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| =150.176 & | ^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 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: 150.176
critical value: 5.991
p-value:0
decision: reject Ho
We hace evidence that there is relationship between health risk and income OR both risk, income is
dependent to each other
col1 col2 col3 row 1 634 332 247 1213 row 2 1846 1622 1868 5336 TOTALS 2480 1954 2115 N = 6549