Question

A researcher records whether n=288n=288 children do or do not have asthma at age 13, and then again records whether these same 288288 individuals have asthma 7 years later. Results are shown in the following table:

	Asthma at age 20?
Asthma at age 13?	Yes	No
Yes	75	22
No	11	180

What is the expected frequency of "asthma at 13" and "asthma at 20"? [Answer to 2 decimal places.]

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What is the expected frequency of "asthma at 13" and "no asthma at 20"? [Answer to 2 decimal places.]

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What is the expected frequency of "no asthma at 13" and "asthma at 20"? [Answer to 2 decimal places.]

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What is the expected frequency of "no asthma at 13" and "no asthma at 20"? [Answer to 2 decimal places.]

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To test whether "asthma at 13" is related to "asthma at 20", what is the value of chi-square test statistic? [Answer to 3 decimal places.]

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Suppose we are testing:

Null hypothesis: "asthma at 13" and "asthma at 20" are not related,
against
Alternative hypothesis: "asthma at 13" and "asthma at 20" are related.

If the p-value associated to the ch-square test-statistics is 0 and the level of significance is 5%, what will be your conclusion?
Not enough information to reach a decision
Do not reject null hypothesis
Reject null hypothesis

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Answer 1

Chi-Square Test
	Observed Frequencies
	column
row	yes	no					Total
yes	75	22					97
no	11	180					191
Total	86	202					288

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	yes	no					Total
yes	28.9653	68.0347					97
no	57.0347	133.9653					191
Total	86	202					288

a)

expected frequency of "asthma at 13" and "asthma at 20" = 86*97/288 = 28.97

b)

expected frequency of "asthma at 13" and "no asthma at 20" = 97*202/288 = 68.03

c)

expected frequency of "no asthma at 13" and "asthma at 20 = 57.03

d)

expected frequency of "no asthma at 13" and "no asthma at 20" = 133.97

e)

	(fo-fe)^2/fe
yes	73.1633	31.1487
no	37.1562	15.8190

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   157.287

p-Value =   0.0000
Decision:    p-value < α , Reject Ho

Reject null hypothesis