Starting in the 1970s, medical technology allowed babies with a very low birth weight (VLBW, less than 1500 grams, or about 3.3 pounds) to survive without major handicaps. It was noticed that these children nonetheless had difficulties in school as adults. A long study has followed 242 randomly selected VLBW babies to age twenty (20) years, along with a control group of 233 randomly selected babies from the same population who had normal birth weight. At age twenty (20), 179 of the VLBW group and 193 of the control group had graduated from high school.

Set up and carry out an appropriate test to determine whether there is convincing evidence that the graduation rate among the VLBW group is significantly lower than for the normal-birth-weight controls. Be sure to provide the type of test used, the correct hypotheses, the test statistic, the P-value, assumptions necessary (if any), and the conclusions in context.

Then, provide and interpret a 95% confidence interval for the hypotheses that you test in (a). What conclusion(s) do you make in context?