Question

9.

The owner of a laboratory wants to keep sick leave as low as possible by keeping employees healthy through disease prevention programs. Since many employees have contracted pneumonia leading to productivity problems due to sick leave from the disease, the owner believes that it is important to get as many employees vaccinated as possible. Half of the employees were given the vaccine, and the number of employees who contracted pneumonia, and whether they were given vaccine or not are summarized in the table below (observed counts table):

Health Outcome	Unvaccinated	Vaccinated	Total
Sick with pneumococcal pneumonia	27	9	36
Sick with non-pneumococcal pneumonia	11	13	24
No pneumonia	62	78	140
Total	100	100	200

What are the degrees of freedom and p-value?

Question 9 options:

	A) df=4, 0.02 < p-value < 0.05
	B) df=3, 0.005 < p-value < 0.01
	C) df=2, 0.001 < p-value < 0.005
	D) df=4, 0.01 < p-value < 0.025
	E) df=2, 0.005 < p-value < 0.001

10.

The owner of a laboratory wants to keep sick leave as low as possible by keeping employees healthy through disease prevention programs. Since many employees have contracted pneumonia leading to productivity problems due to sick leave from the disease, the owner believes that it is important to get as many employees vaccinated as possible. Half of the employees were given the vaccine, and the number of employees who contracted pneumonia, and whether they were given vaccine or not are summarized in the table below (observed counts table):

Health Outcome	Unvaccinated	Vaccinated	Total
Sick with pneumococcal pneumonia	27	9	36
Sick with non-pneumococcal pneumonia	11	13	24
No pneumonia	62	78	140
Total	100	100	200

What is your conclusion in the context of the problem?

Question 10 options:

	A) We have evidence to show that health outcome and vaccination are independent.
	B) We do have evidence to show that health outcome and vaccination are dependent.
	C) We have evidence to show that health outcome and vaccination are positively related.
	D) We do not have evidence to show that health outcome and vaccination are independent.
	E) We have evidence to show that health outcome and vaccination are dependent.

Answer 1

The statistical software output for this problem is:

Contingency table results: Rows: Health Outcome Columns: None Unvaccinated Vaccinated Total Sick with pneumococcal pneumonia 27 36 Sick with non-pneumococcal pneumonia 11 13 24 No pneumonia 62 78 140 Total 100 100 200 Chi-Square test: Statistic DF Value P-value Chi-square 2 10.995238 0.0041

Hence,

Answer - 9: df=2, 0.001 < p-value < 0.005

Option C is correct.

Answer - 10: We have evidence to show that health outcome and vaccination are dependent.

Option E is correct.