In: Statistics and Probability
In 2000, 58% of females aged 15 years of age and older lived alone, according to the U.S. Census Bureau. A sociologist tests whether this percentage is decreased today by conducting a random sample of 500 females aged 15 years of age and older and finds that 280 are living alone. Is there sufficient evidence at the α=0.05 level of significance to conclude the proportion has decreased since 2000? If a random sample of 30 females aged 15 years of age and older and finds that 16 are living alone. Is there sufficient evidence at the α=0.05 level of significance to conclude the proportion has decreased since 2000?