Question

Research suggests that children who grow up with pets are likely to be healthier as adults because they are build up resistance to allergens. Suppose we want to test this theory by asking a sample of n = 60 people whether (a) they had pets during childhood and (b) they have allergies today.

Below is the data from the study:

	Pets	No Pets
Allergies	ƒo = 6	ƒo = 5	11
No Allergies	ƒo = 25	ƒo = 24	49
	31	29	n = 60

1. Compute df and determine the critical value for χ² for a hypothesis test with α = 0.05.

df =
Critical value of χ² =

2. Determine the expected frequencies (ƒ_e) for each of the cells in the table: (Use 3 decimals)
<

	Pets	No Pets
Allergies	ƒe =	ƒe =	11
No Allergies	ƒe =	ƒe =	49
	31	29	n = 60

3. Calculate the chi-square statistic (χ²): (Use 3 decimals)

χ² =

4. What decision should be made?

Retain the null.

Reject the null.    

Answer 1

Solution:

1)

Degree of freedom = (number of row - 1)*(number of columns - 1)

Here 2 rows and 2 columns

Degree of freedom = (2-1)*(2-1)

Degree of freedom = 1

Critical value for with  . Is

Critical value of . From chi square table

2)Table for expected frequency

	Pets	no pets	Total
Allergies			11
No allergies			49
Total	31	29	60

3)

Oi	ei	(oi-ei)	(oi-ei)^2
6	5.683	0.317	0.100489	0.0176823
25	25.317	-0.317	0.100489	0.0039692
5	5.317	-0.317	0.100489	0.0188995
24	23.683	0.317	0.100489	0.0042430
Total				0.0447845

Test statistic

4) Decision

That is 0.045  

Fail to rejecte Ho

Retaine the null