3. A major source of new HIV infections is the passing of the virus from mothers to their infants at the time of birth (due to the infant's exposure to the infected mother's blood). If the infected mother does not receive treatment the probability that she will transmit HIV to her infant is P = 0.3. Researchers are investigating if drugs used to slow the progression from HIV infection to AIDS might reduce this probability of transmission. One of these drugs, AZT, reduces the blood concentration of the virus in infected individuals to very low levels. In a clinical trial, 300 HIV-infected pregnant women were given AZT several times during labor, and the babies given AZT twice daily for 7 days after birth. 75 of the 300 babies in this study tested positive for HIV at 16 weeks of age (P - 0.25). Do these data provide sufficient evidence to conclude that the AZT treatment reduces mother-to-child HIV transmission? (This question is based on Mccarthy, M. 1999. Low-cost drug cuts perinatal HIV-transmission rate. Lancet 354: 309, but has been modified to simplify the analysis). a. State the appropriate Null and Alternative Hypotheses. Ho: Hai b. Describe the sampling distribution of P if the Null hypothesis is true. Scale the X-axis of the distribution to the right in accordance with this description. Shade the area under the curve that corresponds to the p-value for this test of significance. Center: E( P_) = Spread: O p = Shape: C. Explain what this pampling distribution represents in this context using terms someone unfamiliar with statistics could understand. d. Compute the Ztest statistic and determine the p-value. e. Interpret the meaning of this p-value and report your conclusion in terms of the original