According to the U.S. Census Bureau, \(7.1 \%\) of all babies born are of low birth weight ( \(<5 \mathrm{lb}, 8 \mathrm{oz}\) ). An obstetrician wanted to know whether mothers between the ages of 35 and 39 years give birth to a higher percentage of low-birth-weight babies. She randomly selected 240 births for which the mother was 35 to 39 years old and found 22 low-birth-weight babies.

(a) If the proportion of low-birth-weight babies for mothers in this age group is 0.071 , compute the expected number of low-birth-weight births to 35 - to 39 -year-old mothers. What is the expected number of births to mothers 35 to 39 years old that are not low birth weight?

(b) Answer the obstetrician's question at the \(\alpha=0.05\) level of significance using the chi-square goodness-of-fit test.