Question

. In a randomized controlled​ trial, insecticide-treated bednets were tested as a way to reduce malaria. Among 332 infants using​ bednets, 15 developed malaria. Among 270 infants not using​ bednets, 22 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.

Difference= p(1)-p(2)

Estimated for difference: -0.0363008

95% upper bound for difference: 0.00324642

Test for different = 0 (vs < 0): z=-1.84 P-Value= 0.033

What are the null and alternative​ hypotheses?

A. H 0​: p 1 = p2

H 1​: p 1 < p 2

B.H 0​: p 1 ≤ p 2

H 1​: p 1 > p 2

C. H 0​: p 1 = p 2

H 1​: p 1 ≠ p 2

D. H 0​: p 1 ≥ p 2

H 1​: p 1 < p 2

E.H 0​: p 1 ≠ p 2

H 1​: p 1 = p 2

F.H 0​: p 1 = p 2

H 1​: p 1 > p 2

Identify the test statistic. ____

​(Type an integer or decimal rounded to two decimal places as​ needed.)

Identify the​ P-value.____

​(Type an integer or decimal rounded to three decimal places as​ needed.)

What is the conclusion for this​ test?

The​ P-value is (less than/greater than) the significance level a, so (reject/fail to reject)

the null hypothesis. There is (insufficient/sufficient) evidence to support the claim that the incidence of malaria is lower for infants using bednets. The bednets (do not appear/appear) to be effective

Answer 1

To Test :-

D. H 0​: p 1 ≥ p 2

H 1​: p 1 < p 2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 15 + 22 ) / ( 332 + 270 )
= 0.0615

Z = -1.84

Test Criteria :-
Reject null hypothesis if

= -1.84 < -1.64, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z < -1.84 )
P value = 0.0329
Reject null hypothesis if P value <
Since P value = 0.0329 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

The​ P-value is less than the significance level , so (reject)

the null hypothesis. There is (sufficient) evidence to support the claim that the incidence of malaria is lower for infants using bednets. The bednets (appear) to be effective.