Question

hw9 #6

In a randomized controlled​ trial, insecticide-treated bednets were tested as a way to reduce malaria. Among

308308

infants using​ bednets,

1111

developed malaria. Among

254254

infants not using​ bednets,

2525

developed malaria. Use a

0.050.05

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?

Answer 1

Group 1 (Not Using Bed nets)

Sample Size (n1) = 308

Proportion (p1) = 11/308 = 0.0357

Group 2 (Not Using Bed nets)

Sample Size (n2) = 254

Proportion (p2) = 25/254 = 0.0984

pc = (n1*p1 + n2*p2)/(n1+n2) = 0.064

a)

Alpha = 0.05

Null and Alternate Hypothesis

H0: µ1 = µ2

Ha: µ1 > µ2 (Incidence of Malaria is lower in infants using bed nets)

Test Statistic

Z = (p1­ ­– p2­) / (pc*(1-pc)/n1 + pc*(1-pc)/n2 )1/2 = -3.02

P-value (z > -3.02) = 1 – P(z<-3.02) = 1 - 0.0013 = 0.9987

Result

Since the p-value is greater than 0.05, the data is not statistically significant at alpha = 0.05, and we fail to reject the null hypothesis.

Conclusion

Incidence of malaria is same for both groups

b)

pc = (n1*p1 + n2*p2)/(n1+n2) = 0.064

Standard Error (SE) = (pc*(1-pc)/n1 + pc*(1-pc)/n2 )1/2 = 0.020753

Alpha = 0.05

ZCritical = 1.96

Hence,

95% CI for diff of Proportions = p1- p2 +/- SE*ZCritical = 0.0357 – 0.0984 +/- 1.96 * 0.020753 = {-0.103, -0.022}

Result

Since the 95% CI is less than critical value we fail to reject the null hypothesis.

c)

Conclusion

Incidence of malaria is same for both groups ie Bed nets does not seems to be effective

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