Write a two-way table of observed counts for sex and whether a participant in soccer had a lower-extremity injury or not. Determine a two-way table of expected counts for these data. Show calculations verifying that the value of the chi-square statistic is 2.51.

preprekomW 2021-02-06 Answered
Write a two-way table of observed counts for sex and whether a participant in soccer had a lower-extremity injury or not. Determine a two-way table of expected counts for these data. Show calculations verifying that the value of the chi-square statistic is 2.51.
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joshyoung05M
Answered 2021-02-07 Author has 97 answers

a) Here is the table of observed counts:
Gender / Had injury?YesNoTotalMale15315141667Female74925999Total22724392666
The numbers in the ”No” column are simply differences between last column and first column , and the numbers in the last row are sums of columns
b)The expected count for each cell is calculated as
Expected=Total row countTotal column countSample size
Here is the table of the expected counts:
Gender / Had injury?YesNoTotalMale16672272666=141.94166724392666=1525.061667Female9992272666=85.0699924392666=913.94999Total22724392666
c) The value of chi-square statistics is
x2=all cells(Observed countExpected count)2Expected count
=(153141.94)2141.94+(15141525.06)21525.06+(7485.06)285.06+(925913.94)2913.94
=0.8618+0.0802+1.4381+0.1338
=2.5139

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