Please provide complete and detail solutions. Please do it by hand not by comput

Question

Please provide complete and detail solutions. Please do it by hand not by computer software. Thank you!

At study done of 627 patients in a Texas hospital recorded whether or not the patients had Hepatitis C, whether or not they had a tattoo and whether they got that tattoo in a tatoo parlor. The study wants to test whether getting a tattoo is related to Hepatitis C infection. Perform the appropriate x^2 test, and interpret your result. Why would it be wrong to conclude that tattoo parlors are responsible for Hepatitis C? Perform a test that specifically compares the rate of Hep C in people who went to tattoo parlors to the rest of the population of people.

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 =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 = 62.69
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| =62.69 & | ^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: 62.69
critical value: 5.991
p-value:0
decision: reject Ho      

tattoo is related to Hepatitis C infection.                   

col1 col2 row 1 18 35 53 row 2 8 53 61 row 3 22 491 513 TOTALS 48 579 N = 627

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