Question

Researchers studied a random sample of high school students who participated in interscholastic athletics to learn about the risk of lower-extremity injuries (anywhere between hip and toe) for interscholastic athletes. Of 998 participants in girls' soccer, 77 experienced lower-extremity injuries. Of 1660 participants in boys' soccer, 159 experienced lower-extremity injuries.

Write a two-way table of observed counts for gender and whether a participant had a lower-extremity injury or not.

Gender	Had Injury	No Injury	Total
Girls
Boys
Total

(b) Determine a two-way table of expected counts for these data. (Round the answers to one decimal place where it is needed.)

Gender	Had Injury	No Injury	Total
Girls
Boys
Total

(c) Show calculations verifying that the value of the chi-square statistic is 2.67. Chi-square = (77-88.6)2/ + (921- )2/909.4 + ( -147.4)2/147.4 + (1501- )2/ = 1.52 + 0.15 + + 0.09 = 2.67

Answer 1

In this problem the given data are -

I) Out of 998 girl participants 77 girls became injured.

So, number of injured girls = 77 and number of not injured girls = 921

II) Out of 1660 boys participants 159 became injured

So, number of injured boys participants = 159 and number of not injured boys participants =1501

Therefore our Chi-square 2x2 contingency table of observed counts for gender and whether a participant had a lower-extremity injury or not becomes

Table 1

Gender	Had Injury	No Injury	Total
Girls	77	921	998
Boys	159	1501	1660
Total	236	2422	2658

Table 1 is the table of observed values.

Now we construct Table 2 of expected values.

Table 2

Gender	Had Injury	No Injury	Total
Girls	88.6	909.4	998
Boys	147.4	1512.6	1660
Total	236	2422	2658

We have made this table by making a little bit changes in the previous table.

Now the formula of calculating Chi-square statistic is =

  

Now the value of Chi-Square statistic is =

=1.52 + 0.15 + 0.91 + 0.09

=2.67

So the value of Chi-Square statistic is 2.67.