A study was conducted to examine if asthma occurs more often for children with smoking mothers: Of the 600 children age 0-4 with smoking mothers, 17 of them were had asthma over the past one year. Suppose the annual incidence of asthma (1$ ") is 2.0% for children age 0-4 from the general population. a. [3 points] Construct a 95% confidence interval for p, where p is the annual incidence of asthma for children age 0-4 with smoking mothers. b. [3 points] Test the hypothesis on whether smoker mother would increase the annual incidence of asthma at a = 0.05. C. [4 points] if we don't know any information about the asthma, could you find the sample size n so that the length of 90 percent confidence interval for p is at most 0.04 [Length of confidence interval equal 2*Margin of Error] Hints: Note that ( 4 ) ( 1 - 4 ) = J() ( 1 -;) d. [5 points] For Reconfirm the Result, we collect a new sample of 10 children age 0-4 with smoking mothers and find that 2 of them had asthma over the past one year. Test the hypothesis on whether smoker mother would increase the annual incidence of asthma based on the new sample at a = 0.05 Hints: Use exact method and calculate its p-value. The mean birth weight in the United States in 2010 is M = 3315 grams with a standard deviation of o = 575. After 10 years, the health department claims that that birth weight would reduce u