Question

A researcher records whether n=280n=280 children do or do not have asthma at age 13, and then again records whether these same 280280 individuals have asthma 7 years later. Results are shown in the following table:

	Asthma at age 20?
Asthma at age 13?	Yes	No
Yes	85	17
No	5	173

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.]

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.

6. 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?
A. Do not reject null hypothesis
B. Reject null hypothesis
C. Not enough information to reach a decision

Answer 1

The table showing the records whether children having asthma at the age of 13 do or do not have asthma at the age of 20 is shown in the table below.

	Asthma at the age of 20?
Asthma at the age of 13	Yes	No	Total
Yes	85	17	102
No	5	173	178
Total	90	190	280

To find the expected frequencies, we use the formula,

1. Expected frequency of asthma at 13 and asthma at 20 is given by,

2. Expected frequency of asthma at 13 and no asthma at 20 is given by,

3. Expected frequency of no asthma at 13 and asthma at 20 is given by,

4. Expected frequency of no asthma at 13 and no asthma at 20 is given by,