(Solved): Please explain step by step Birthweight. In 2003 the Journal of the American Medical Association rep ...

Birthweight. In 2003 the Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the \( 9 / 11 \) attack on New York's World Trade Center on the weight of babies. Researchers found that \( 8 \% \) of 186 babies born to mothers exposed to heavy doses of soot and ash on that day were classified as having low birth weight. \( 4 \% \) of 2300 babies born to mothers who had not been near the site of the disaster were classified as having low birth weight. Testing at the \( .01 \) level of significance, can one conclude that the air pollution is linked to a higher proportion of lowbirthweight babies? a) Test Design. Using the proper symbols and syntax, state the type of test this is, the null hypothesis, the alternate hypothesis, and the significance level for this problem. b) Test Statistic. What is the value of the test statistic? c) P-value. What is the p-value for this problem? Also include the \( \mathrm{p} \)-value plot. d) Decision. Should you reject \( \mathrm{H}_{0} \) or not reject \( \mathrm{H}_{0} \) ? What is the reasoning for your reject/do-not-reject decision? (Back it up with appropriate numbers.) e) Interpretation. State your interpretation for your reject/do-not-reject decision in the context of the problem. f) Retrospective. Would your decision be different if you had run a two-tailed test? (Back it up with appropriate numbers.)