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. In Problems 25 and 26, we test hypotheses with the use of both methods.
Low Birth Weight According to the U.S. Census Bureau, 7.1% of all babies born are of low birth weight . 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?

"In Problems 17–20, determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.

Length of Phone Calls The relative frequency histogram represents the length of phone calls on my wife’s cell phone during the month of September. "

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. In Problems 25 and 26, we test hypotheses with the use of both methods.

Living Alone? In 2000, 25.8% of Americans 15 years of age or older lived alone, according to the Census Bureau. A sociologist, who believes that this percentage is greater today, conducts a random sample of 400 Americans 15 years of age or older and finds that 164 are living alone.

a. If the proportion of Americans aged 15 years or older living alone is 0.258, compute the following expected numbers: Americans 15 years of age or older who live alone; Americans 15 years of age or older who do not live alone.