in a report healthy people 2020 objective for the nation, the centers for disease control and prevention CDC set a goal of 0.341 for the proportion of mothers who will still be breastfeeding their babies one year after birth. the CDC also estimated the proportion who were still being breastfed one year after birth to be 0.307 for babies born in 2013. this estimate was based on a survey of women who had given birth in 2013. suppose that he survey used a random sample of 1000 mothers and that you want to use the survey data to decide if there is evidence that the goal is not being met. let p denote the population proportion of all mothers of babies born in 2013 who were still breastfeeding at 12 months. use a table or SALT

a. describe the shape, center, and variability of the sampling distribution of p for random samples of size 1000 if the null hypothesis Ho: p=0.341 is true. round your standard deviation to four decimal places. the sampling distribution is centered at Yp=_____. the standard deviation of the sampling distribution is Op=______.

b .would you be surprised to observe a sample proportion as small as p= 0.334 for a sample of sample of size 1000 if the null hypothesis Ho: p=0.341 were true? round answer to four decimal places. the probability of a sample proportion this small is ______ if the acceptance level of 0.05.

c. would you be surprised to observe a sample proportion as small as p= 0.309 for a sample of size 1000 if the null hypothesis Ho: p=0.341 were true? the probability of a sample proportion this small or smaller is _____ which the acceptance level is 0.05.

d. the actual sample proportion observed in the study was p=0.307. based on this sample proportion, is there convincing evidence that the goal is not being met, or is the observed sample proportion consistent with what you would expect to see when the null hypothesis is true? support your answer with a probability calculation. round answer to four decimal places. since probability of a sample proportion this small or smaller is _____ which is ___ the acceptance level of 0.05 there is ___convincing evidence that the goal is not being met.