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 = 40 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 = 9	ƒo = 10	19
No Allergies	ƒo = 16	ƒo = 5	21
	25	15	n = 40

1. Compute df and determine the critical value for χ² for a hypothesis test with α = 0.01.

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 =	19
No Allergies	ƒe =	ƒe =	21
	25	15	n = 40

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

(1) The degrees of freedom, df = (r – 1) * (c -1) = (2 - 1) * (2 - 1) = 1

The Critical Value:   The critical value at = 0.01 ,df = 1

critical = 6.635

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(2) The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 40

Expected
	Pets	No Pets	Total
Allergies	19.250	13.750	33
No Allergies	15.750	11.250	27
Total	35	25	60

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(3) The Test Statistic:

Number	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	15	19.25	-4.25	18.063	0.9383
2	20	15.75	4.25	18.063	1.1468
3	18	13.75	4.25	18.063	1.3136
4	7	11.25	-4.25	18.063	1.6056
Total					5.0043

test = 5.004

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(4) Since test is >< c, We Retain The Null

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