In randomized controlled trial, insecticide-treated bednets were tested as way t

Question

In randomized controlled trial, insecticide-treated bednets were tested as way to reduce malaria. Among 307 infants using bednets, 11 developed malaria Among 268 infarcts 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. Do the bednets appear to be effective? Conduct the hypothesis test by using the results from the given display. Based on the test statistic given above, find the P-value Rounded to three decimal places as needed.) What is the conclusion for this test? The P value is less than the significance level a so the bednets do not appear to be effective

Explanation / Answer

Given that,
sample one, x1 =11, n1 =307, p1= x1/n1=0.036
sample two, x2 =23, n2 =268, p2= x2/n2=0.086
null, Ho: p1 = p2
alternate, H1: p1 < p2
level of significance, = 0.05
from standard normal table,left tailed z /2 =
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.036-0.086)/sqrt((0.059*0.941(1/307+1/268))
zo =-2.535
| zo | =2.535
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =2.535 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: left tail - Ha : ( p < -2.5352 ) = 0.00562
hence value of p0.05 > 0.00562,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 < p2
test statistic: -2.535
critical value: -1.645
decision: reject Ho
p-value: 0.00562

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