Question

A survey reveals that trauma patients who seek care at an urban health and wellness clinic experienced differing rates of wound healing. Specifically, over a 4-week period, 40% reported 0-25% wound healing, 30% reported 26-50% wound healing, 20% reported 51-75% wound healing, and 10% reported 76-100% wound healing. Researchers recruit a sample of 250 participants into an observational study and assesses their wound healing again after 4-weeks. The results are displayed in the table below:

Percent Wound Healing	0-25%	26-50%	51-75%	76-100%
Number of Patients	110	70	50	20

Is there evidence at the 5% level to suggest that the distribution of wound healing in this sample is different from those from the previous study?

a. Set up hypotheses and determine level of significance

b. Compute the test statistic

c. Compute expected values

Answer 1

Expected Values are calculated for different classes by multiplying by expected percentage to 250 i.e. for class 0-25% expected frequency = 250*0.4 and similarly values are calculated for other classes.

Percent Wound Healing	Observed Frequency	Expected frequency	(Oi - Ei)^2/Ei
0-25%	110	250 * 0.4 = 100	1
26-50%	70	250 * 0.3 = 75	0.33
51-75%	50	250 * 0.2 = 50	0
76-100%	20	250 * 0.1 = 25	1
			2.33

Test statistic, chi-square = sum((Oi - Ei)^2/Ei) = 2.33

Significance level is 0.05

p-value = 0.5062

As p-value > 0.05, fail to reject H0

There are not significant evidence to conclude that the distribution is different from those from the previous study