Is the home field advantage independent of the sport? Winning team data were col

Question

Is the home field advantage independent of the sport? Winning team data were collected for teams in different sports. Use 0 .05 for alpha to test the claim that "home team wins" vs. "visiting team wins" are independent of the sport. Write A Complete Answer! Compute the "home team winning percentage" for each sport. Use these percentages to explain the conclusion of the hypothesis test !! (Minimum of THREE complete sentences !) List the " Expected Values " used in the Chi - Square Hypothesis Test Use these values to explain the conclusion of the hypothesis test (Minimum of THREE complete sentences !)

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 =7.815
since our test is right tailed,reject Ho when ^2 o > 7.815
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 4.233
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 4 - 1 ) = 1 * 3 = 3 is 7.815
we got | ^2| =4.233 & | ^2 | =7.815
make decision
hence value of | ^2 o | < | ^2 | and here we do not reject Ho
^2 p_value =0.237
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: 4.233
critical value: 7.815
p-value:0.237
decision: do not reject Ho                              

col1 col2 col3 col4 row 1 127 53 50 57 287 row 2 73 47 43 43 206 TOTALS 200 100 93 100 N = 493

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