Question

A clinical trial is run to investigate the effectiveness of an experimental drug in reducing preterm delivery to a drug considered standard care and to placebo. Pregnant women are enrolled and randomly assigned to receive either the experimental drug, the standard drug or placebo. Women are followed through delivery and classified as delivering preterm (< 37 weeks) or not. The data are shown below.

Preterm Delivery	Experimental Drug	Standard Drug	Placebo
Yes	20	32	36
No	80	68	64

a) Is there a statistically significant difference in the proportions of women delivering preterm among the three treatment groups? Run the test at a 5% level of significance.(hint: χ2 test) (10 points)

Ho:                                                        VS   H1:

Compute : χ² (7 points):

P-value(1 point)

Conclusion(1 points):

                       Accept H0                                                                      Reject H0         

Answer 1

Ho:

there is no difference in the proportions of women delivering preterm among the three treatment groups

Ha: there is a statistically significant difference in the proportions of women delivering preterm among the three treatment groups

Applying chi square test:

	Oi	Experimental	Standard Drug	Placebo	Total
	Yes	20	32	36	88
	not meet	80	68	64	212
	total	100	100	100	300
Expected	Ei=row total*column total/grand total	Experimental	Standard Drug	Placebo	Total
	Yes	29.333	29.333	29.333	88
	not meet	70.667	70.667	70.667	212
	total	100	100	100	300
chi square    χ2	=(Oi-Ei)2/Ei	Experimental	Standard Drug	Placebo	Total
	Yes	2.9697	0.2424	1.5152	4.727
	not meet	1.2327	0.1006	0.6289	1.962
	total	4.202	0.343	2.144	6.6895

χ² =6.6895

degree of freedom(df) =(rows-1)*(columns-1)=

2

for 2 degree of freedom and above test statistic ; p value =0.0353

Conclusion:Reject Ho