Question

A researcher records whether n = 247 children do or do not have asthma at age 13, and then again records whether these same 247 individuals have asthma 7 years later. Results are shown in the following table:

	Asthma at age 20?
Asthma at age 13?	Yes	No
Yes	55	16
No	12	164

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

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

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

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

5. 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.]

Answer 1

as expected frequency =row total*column total\/grand total

1)

expected frequency of "asthma at 13" and "asthma at 20" =67*71/247 =19.26

2)expected frequency of "asthma at 13" and "no asthma at 20"=51.74

3)expected frequency of "no asthma at 13" and "asthma at 20" =47.74

4) expected frequency of "no asthma at 13" and "no asthma at 20" =128.26

5)

applying chi square test:

chi square    χ2	=(Oi-Ei)2/Ei	yes	no	Total
	yes	66.3276	24.6886	91.016
	no	26.7572	9.9596	36.717
	total	93.085	34.648	127.733

value of chi-square test statistic =127.733

( please try 127.724 if this comes wrong due to rounding error)