The article "Breast-Feeding Rates Up Early" (USA Today, Sept. 14,2010 )
summarizes a survey of mothers whose babies were born in \(2009 .\) The Center
for Disease Control sets goals for the proportion of mothers who will still be
breast-feeding their babies at various ages. The goal for 12 months after
birth is 0.25 or more. Suppose that the survey used a random sample of 1,200
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 proportion of all
mothers of babies born in 2009 who were still breast-feeding at 12 months.
(Hint: See Example 10.10 )
a. Describe the shape, center, and spread of the sampling distribution of
\(\hat{p}\) for random samples of size 1,200 if the null hypothesis \(H_{0}:
p=0.25\) is true.
b. Would you be surprised to observe a sample proportion as small as
\(\hat{p}=0.24\) for a sample of size 1,200 if the null hypothesis \(H_{0}:
p=0.25\) were true? Explain why or why not.
c. Would you be surprised to observe a sample proportion as small as
\(\hat{p}=0.20\) for a sample of size 1,200 if the null hypothesis \(H_{0}:
p=0.25\) were true? Explain why or why not.
d. The actual sample proportion observed in the study was \(\hat{p}=0.22 .\)
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.
