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

Step-by-step explanation:

Given that 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.

H0: p1=p2

H1: p1 <p2

(one tailed test)

p1 = 15/343:p2 =27/294:

Difference4.813 %

95% CI0.9160% to 9.0217%

Chi-squared5.947

DF  1

Significance levelP = 0.0073

Since p <0.01 we reject null hypothesis.

We are given that

a and b are integers and 71 < ab < 76

We will check each options

option-A:

b=18

we can plug it

we can divide both sides by 18

now, we can simplify it

Since, 'a' is a integer

so, a=4 lies on interval

so, this interval is true

so, this is FALSE

option-B:

b=8

we can plug it

we can divide both sides by 8

now, we can simplify it

Since, 'a' is a integer

so, a=9 lies on interval

so, this interval is true

so, this is FALSE

option-C:

b=12

we can plug it

we can divide both sides by 12

now, we can simplify it

Since, 'a' is a integer

so, a=6 lies on interval

so, this interval is true

so, this is FALSE

option-D:

b=7

we can plug it

we can divide both sides by 7

now, we can simplify it

Since, 'a' is a integer

so, no integer lies on this interval

so, this interval is false

so, this is TRUE

option-E:

b=5

we can plug it

we can divide both sides by 5

now, we can simplify it

Since, 'a' is a integer

so, a=15

so, this interval is true

so, this is FALSE