Question

problem that causes abnormally small heads, among other things There are strong concerns that the Zika virus can cause microcephaly. Detecting microcephaly in can help expectant parents be prepared. Head diameter measurements can be made in utero ultrasound at 20 weeks. Bipariet fetal head) measurements were taken on 71 newborn infants with exposure to Zka and suspected to have microcephaly (they were eventually confirmed at birth to have microcephaly). The sample mean 34 mm. The sample standard deviation is 5 mm 1) is this sample a biased or unbiased representation of the microcephaly population? Explain. (4) 2) Are the sample statistics (mean & s.d.) biased or unbiased estimates of the population? Explain (1) tal Diameter (BPD, the distance between the two parietal bones of Low BPD is an indicator of the microcephaly disorder, but some kids also just have low BPD without any disorder. It is helpful to know the range of "normal" head sizes 71 head measurements were collected from 20-week ultrasounds at the same hospitals as the first sample, from demographically-similar mothers that were expected to have similar exposure to Zika. The sample mean was 48 mm and s-27 3) Explain why this sample could be a biased representation of BPD in normal, healthy babies. (1) 4) Explain why the researchers might still prefer to use these data for comparison to the first sample, despite potential bias (1) ) Use a statistical test to compare these two samples, report the results, and interpret those results without statistical jargon. (3) A completely randomized (unbiased) sample of 100 BPD measurements had a mean of 52 mm and standard deviation of 7 mm 6) Is the variance of this sample significantly different from the 71 demographically-similar but healthy babies mentioned above? use an appropriate hypothesis test to support your answer. (2) Using this sample of 100 BPD measurements, test the (alternative) hypothesis that 20-week BPD is lower in microcephaly babies. (2) Some have suggested that ndividuals in the lowest 1% of-normal" 20-week BPD measurements should be further screened for genetic defects. What is the cutoff value for this criterion, based on the sample of 100 BPD measurements?(1) 7) 8) 9) Based on the sample of 71 microcephaly babies, what proportion of babies with microcephaly will have a BPD lower than the cutoff from part (hj? (1) What proportion of babies without microcephaly will have a BPD lower than the cutoff? (1) 10) An expecting mother has an ultrasound and her baby is found to have a BPD of 30. 11) What is the probability of a healthy baby having a BPD of 30 or lower? (1) 12) What is the probability of a microcephalic baby having a BPD of 30 or lower?(1) 13) Approximately 7 babies out of 100,000 babies born in the US have microcephaly. If this mother is n the US, what is the probability that this baby has microcephaly? (2) 14) razil saw a huge increase in microcephaly during its worst Zika outbreak, with-25,000 crocephaly cases in one year (birth rate in Brazil is 3 million births/year), If this mother is in Brazil, what is the probability that this baby has microcephah? (21

Answer 1