Question

Use the contingency table to the right to calculate the marginal frequencies and find the expected frequency for each cell in the contingency table. Assume that the variables are independent.		Athlete has
	Result	Stretched	Not stretched
	Injury	17	25
	No injury	202	182

​(a) Calculate the marginal frequencies and sample size.

	Athlete has
Result	Stretched	Not stretched	Total
Injury	17	25	nothing
No injury	202	182	nothing
Total	nothing	nothing	nothing

​(b) Find the expected frequency for each cell in the contingency table.

	Athlete has
Result	Stretched	Not stretched
Injury	nothing	nothing
No injury	nothing	nothing

​(Round to two decimal places as​ needed.)

Answer 1

a) Answer :

The marginal frequencies are given in the table below.

	Stretched	Not Stretched	Total
Injury	17	25	17 + 25 = 42
No injury	202	182	202 + 182 = 384
Total	17 + 202 = 219	25 + 182 = 207	42 + 384 = 426

b) Answer :

The expected frequency is given in the table below.

	Stretched	Not Stretched	Total
Injury	21.59	20.41	42
No injury	197.41	186.59	384
Total	219	207	426

The expected frequency for a cell is calculated by

value = (row total * column total) / grand total

The value for athlete has stretched and result is injury = (219 * 42) / 426 = 21.59

The value for athlete has not stretched and result is injury = (207 * 42) / 426 = 20.41

The value for athlete has stretched and result is not injury = (219 * 384) / 426 = 197.41

The value for athlete has not stretched and result is not injury = (207 * 384) / 426 = 186.59