Question

1.   This two-way table summarizes data about the occurrences of two patient measurements in combination: blood pressure (BP - HIGH BLOOD PRESSURE AND NORMAL BLOOD PRESSURE) and cholesterol level (C - HIGH CHOLESTEROL AND NORMAL CHOLESTEROL) for 53 individuals who were measured at the infirmary of a large steel mill as part of their annual check-ups (these are the observed values):

High BP Normal HBP) BP (NBP) High Cholesterol HC) Normal Cholesterol (NC) 13 21

a) What are the expected values for each of the conditions (ie, HC/HBP, HC/NBP, NC/HBP and NC/NBP)?

b) What is the value of the Chi Square test? Be sure to show your work in order for partial credit to be given if part of your calculations are off.

c) What is the critical value?

d) Is this test significant or not, and why?

e) What can we conclude about the outcome?

Answer 1

Null Hypothesis H0: The BP is independent of Cholesterol level

Alternative Hypothesis H1: The BP depends on Cholestrol level

a) Under H0, the expected frequencies are

	Obs. Freq ( O)			Exp. Freq. ( E )
	HBP	NBP	Total	HBP	NBP	Total
High Cholestrol	13	11	24	9.51	14.49	24
Normal Cholestrol	8	21	29	11.49	17.51	29
Total	21	32	53	21	32	53

E(HC/HBP) = 21*24/53 = 9.51

E(HC/NBP) = 24-9.51=14.49

E(NC/HBP) = 21 -9.51 =11.49

E(NC/NBP) = 32-14.49=17.51

b) Under H0, the chi square test statistic and calculations are given below:

	Obs (Freq. ( O )	Exp. Freq. ( E )	(O-E)^2/E
	13	9.51	1.2808
	11	14.49	0.8406
	8	11.49	1.0601
	21	17.51	0.6956
Total	53	53	3.8770

c) Degrees of Freedom = (r-1)*(c-1) = (2-1)*(2-1) = 1

Significance Level $\alpha =0.05$

The critical value of chi square for 1 df at 5% significance level is 3.841

d) Since the value of Chi square statistic is greater than Chi square calculated. it is significant and null hypothesis is rejected.

e) Hence we conclude that

e) The BP depends on Cholestrol level