Question

In a randomized controlled trial in Kenya, insecticide treated bed nets were tested as a way to reduce malaria. Among 343 infants using bed nets, 15 developed malaria. Among 294 infants not using bed nets, 27 developed malaria (based on data from “Sustainability of Reductions in Malaria Transmission and Infant Mortality in Western Kenya with use of insecticide treated bed nets, Journal of the American Medical Association, Vol. 291, No. 21) a) Construct a 99% confidence interval for the difference in proportions between the two populations. You decide which population is population 1 and which is population 2 b) Based on your results do bed nets appear to be effective?

Answer 1

Population 1 :  Infants not using bed nets

Population 2 :  Infants using bed nets

Confidence interval for the difference in proportions between the two populations:

Sample 1 : Infants not using bed nets.

Sample size : Number of Infants using bed nets : n₁= 294

Number of infants who developed Malaria : x₁ = 27

Proportion of infants using bed nets developed Malaria : = 27/294 = 0.0918

Sample 2 : Infants using bed nets.

Sample size : 2 : Number of Infants using bed nets : n₂= 343

Number of infants who developed Malaria : x₂ = 15

Proportion of infants using bed nets developed Malaria : = 15/343 = 0.0437

Confidence Level	99%
(= 100-99/100=1/100 ) = 0.01	0.01
/2 (=0.01/2=0.005)	0.005
	2.5758

99% confidence interval for the difference in proportions between the two populations:

99% confidence interval for the difference in proportions between the two populations: (-0.0038, 0.1)

b) As '0' is within the 99% confidence interval which indicates that there is not sufficient evidence to conclude  the difference in the proportion between two populations is not zero ; i.e. the difference in the proportion of Malaria development between infants using bed nets and not using bet nets is not significant.

Hence ,

Bed nets do not appear to be effective.