QuestionIn a randomized controlled trial, insecticide-treated bednets were tested as a way to reduce malaria. Among 322 infants using bednets, 10 developed malaria. Among 252 infants not using bednets, 23 developed malaria. Use a 0.05 significance level to test the claim that the incidence of malaria is lower for infants using bednets. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. Based on the results, do the bednets appear to be effective? a. What are the null and alternative hypotheses?
Let the infants using bednets be sample 1 and let the infants not using bednets be sample 2. Choose the correct hypotheses below. A. $H_{0}: p_{1}=p_{2}$ B. $H_{0}: p_{1} \leq p_{2}$ C. $H_{0}: p_{1} \geq p_{2}$ $H_{1}: p_{1} \neq p_{2}$ $H_{1}: p_{1}>p_{2}$ $H_{1}: p_{1}<p_{2}$ D. $H_{0}: p_{1}=p_{2}$ E. $H_{0}: p_{1}=p_{2}$ $H_{1}: p_{1}>p_{2}$ $H_{1}: p_{1}<p_{2}$ F. $H_{0}: p_{1} \neq p_{2}$ $H_{1}: p_{1}=p_{2}$
Identify the test statistic. -3.07 (Round to two decimal places as needed.) Identify the P -value. .001 (Round to three decimal places as needed.)
What is the conclusion for this test? Since the P -value is $\square$ less than the significance level $\alpha$, $\square$ reject the null hypothesis. b. Let the infants using bednets be sample 1 and let the infants not using bednets be sample 2 . Use a 0.05 significance level to construct a confidence interval. $\square$ $<\left(p_{1}-p_{2}\right)<$ $\square$ (Round to three decimal places as needed.)