4. According to a study in 2014 , in 16% of all homes with a stay-at-home parent, the father is the stay-at-home parent. An independent research wants to conduct a sample survey to evaluate the proportion for this year. (a) (6 points) If the researcher wants to estimate it with a 95% confidence interval and the margin of error should be less than 3%, what sample size is needed? (b) (10 points) Suppose the researcher ended in getting 200 samples and the sample proportion is 19%. Can we say that the proportion of fathers staying at home is higher than that in2014? Please conduct the hypothesis test with significance level 0.05 ( 5 steps). (c) (6 points) What is the p-value for the test in (b)