A report set a goal of 0 541 for the proportion of babies still being breastfed one year after birth The organization also used the survey data to estimate the proportion who were still being breastfe one year after birth to be 0 351 for babies born in a particular year Suppose that the survey used a random sample of 1 000 parents 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 babies born in that particular year who were still breastfeeding at 12 months Hint See Example 10 10 USE SALT The shape of the sampling distribution is approximately normal The sampling distribution is centered at 0 541 0 0158 MY NOTES a Describe the shape center and variability of the sampling distribution of p for random samples of size 1 000 if the null hypothesis Ho P 0 541 is true Round your standard deviation to four decimal places PRACTICE ANOTH The standard deviation of the sampling distribution is b Would you be surprised to observe a sample proportion as small as p 0 532 for a sample of size 1 000 if the null hypothesis Ho p 0 541 were true Explain why or why not Round your answer to four decimal places Consider the event surprising if the probability the event occurs when Ho p 0 541 is true is less than 0 05 We would not 0 be surprised to observe a sample proportion of p 0 532 for a sample of size 1 000 if the null hypothesis Ho p 0 541 is true The probability of a sample proportion this small or smaller is 0 2843 which is greater than 0 05 c Would you be surprised to observe a sample proportion as small as p 0 507 for a sample of size 1 000 if the null hypothesis Ho p 0 541 were true Explain why or why not Round your answer to four decimal places Consider the event surprising if the probability the event occurs when Ho p 0 541 is true is less than 0 05 Since the probability of a sample proportion this small or smaller is 0 met We would 0 be surprised to observe a sample proportion of p 0 507 for a sample of size 1 000 if the null hypothesis Ho p 0 541 is true The probability of a sample proportion this small or smaller is 0 006 X which is less than 0 05 d The actual sample proportion observed in the study was p 0 351 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 Round your answer to four decimal places Consider the evidence that the goal is not being met convincing if the probability the event occurs when Ho P 0 541 is true is less than 0 05 which is less than O 0 05 there is convincing evidence that the goal is not being