According to the U.S. Census Bureau, 7.1% of all babies born are of low birth weight (<5 lb, 8 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 a = 0.05 level of significance using the chi-square goodness-of-fit test.

(c) Answer the question by using the approach presented in Section 10.2.

We tested hypotheses regarding a population proportion using a z-test. However, we can also use the chi-square goodness-of-fit test to test hypotheses with k = 2 possible outcomes.