STAT 218 Quiz 1-2

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University of Nebraska, Lincoln *

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Feb 20, 2024

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Quiz 1 Total score: 27 In the United States, mothers who live in poverty generally have babies with lower birth weight than those who do not live in poverty. While the average birth weight for babies born in the U.S. is approximately 7.5 pounds, the average birth weight for women living in poverty is 6.17 pounds. Eliminating the linkage between poverty and low birth weight status has been a prominent dimension of health policy for the past decade. Recently, a local hospital introduced an innovative new prenatal care program to reduce the number of low birth weight babies born in the hospital. In the first year, 25 mothers, all of whom live in poverty, participated in this program. Data drawn from hospital records reveals that the babies born to these women had a birth weight of 6.78 pounds, with a standard deviation of 1.1 pounds. (a) What are the observational units? (1 pt) The babies and their weight (b) Write the null and alternative hypotheses in words and in symbols (4 pts) H 0 : u=6.17 H a : u>6.17 Null: The long run average weight of newborn babies from mothers in poverty is 6.17 pounds Alternative: The long run average weight of newborn babies form mothers in poverty is more than 6.17 pounds
(c) What is the parameter of interest (in words) and what is the statistic (value) (2 pts)? Parameter: average weight of newborn babies whose mothers are in poverty Stat: 6.78 pounds (d) Compute a standardized statistic. (4) T= 6.78 − 6.17 1.1 √ 25 = 2.773 (e) Based on the standardized statistic and/or p- value, make A DECISION (regarding the null hypothesis) and A CONCLUSION for a general reader. (2 pts) -Reject the Null hypothesis because t=2.773 > that the critical value=2 -the long run average weight of newborn babies from mothers in poverty is greater than 6.17 pounds. (f) Calculate a 95% confidence interval and interpret it. (4+2) 6.78 ± 2 x 2.773 (-1.234, 12.236) With 95% confidence, the long run average weight of newborn babies from mothers in poverty will fall between the interval (-1.234, 12.236). (g) What is the Type I error in this scenario? Write its consequence. (2+2) The type one error would be to reject the null of u=6.17, and it would mean that there would be less benefits out there for underweight babies from mothers in poverty
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