Question

In a randomized controlled trial in Kenya, insecticide-treated bednets were tested as a way to reduce malaria. Among 343 infants using bednets, 15 developed malaria. Among 294 infants not using bednets, 27 developed malaria. Want to use a 0.01 significance level to test the claim that the incidence of malaria is lower for infants using bednets. Find the test statistic. (Round to the nearest hundredth) (ONLY TYPE IN THE NUMBER!)

Answer 1

Answer: In the given question, we are to test if the population proportion of infants using bednets is lesser than those of not using bednets. To test this, we construct our null and alternative hypothesis as:

H0: p1 = p2 vs Ha: p1 < p2, where p1 and p2 are the unknown population proportions of infants developing malaria with and without the usage of bednets. The test statistic for the above test is: Z = (p1_hat - p2_hat) / sqrt( p * (1-p) * (1/n1 + 1/n2))

where p1_hat and p2_hat are the sample proportions,i.e., The sample proportions are p₁-hat = x1 / n₁ and p₂-hat = x2/ n₂ . x1 and x2 being the number of infants infected with malaria in the with and without bednet groups respectively. n1 and n2 are the sample sizes and p = (x1+x2)/(n1+n2),

Under H0, Z ~ N(0,1).

We reject H0 if Z(observed) < - tau(alpha) where tau(alpha) is the upper alpha point of a standard normal distribution.

Here Z(observed) = -2.44 (rounded to nearest hundredth) and -tau(alpha) =  -1.644.

Thus, Z(observed) < - tau(alpha).

So, we reject H0 and conclude on the basis of the given sample measures at 5% level of significance that there is sufficient evidence to accept the claim that the incidence of malaria is lower for infants using bednets than those not using bednets.

(The answers are obtained using R-software. Code and output are attached for verification).