Question

In a study, 2,017 high school students were questioned on the prevalence of symptoms of severe cold at the age of 15 and again, two years later at the age of 17 years. Was there a significant difference in the prevalence of severe cold at the two ages? Use a 5% level of significance. Give each of the following to receive full credit: 1) the appropriate null and alternative hypotheses; 2) the appropriate test; 3) the decision rule; 4) the calculation of the test statistic; and 5) your conclusion including a comparison to alpha or the critical value. You MUST show your work to receive full credit. Partial credit is available.

Severe colds at age 15

Severe colds at age 17 Yes No

Total

Yes	399	266	665
No	307	1045	1352
Total	706	1311	2017

Answer 1

1) the appropriate null and alternative hypotheses

Null hypotheses: There is no association between the two ages of severe cold.

Alternative hypotheses: There is an association between the two ages of severe cold.

2) the appropriate test

		Observed (O)
		Severe colds at age 17
		Yes	No	Total
Severe colds at age 17	Yes	399	266	665
	No	307	1045	1352
	Total	706	1311	2017
		Expected ( E)
		Severe colds at age 17
		Yes	No
Severe colds at age 17	Yes	232.766485	432.23352
	No	473.233515	878.76648
		(E-O)^2/E
		Severe colds at age 17
		Yes	No
Severe colds at age 17	Yes	118.718043	63.932066
	No	58.3931202	31.445876

The test statistic is

The p-value for the Chi-square=272.486 for (2-1)(2-1)=1 is 0.000.

3) Decision: The p-value 0.000 is less than a 5% level of significance. Hence, reject the null hypothesis.

4) Conclusion: There is a significant difference in the prevalence of severe cold at the two ages.