For at least the past 20 years, there has been a debate over whether children who are placed in child-care facilities while their parents work suffer as a result. A recent study of 6,000 children discussed in Developmental Psychology found “no permanent negative effects caused by their mothers’ absence.” In fact, the study indicated that there might be some positive benefits from the day-care experience. To investigate this premise, a nonprofit organization called Child Care Connections conducted a small study in which children were observed playing in neutral settings (not at home or at a day-care center). Over a period of 20 hours of observation, 15 children who did not go to day care and 21 children who had spent much time in day care were observed. The variable of interest was the total minutes of play in which each child was actively interacting with other students. Child Care Connections leaders hoped to show that the children who had been in day care would have a higher median time in interactive situations than the stay-at-home children. The file Children contains the results of the study.
a. Conduct a hypothesis test to determine if the hopes of the Child Care Connections leaders can be substantiated. Use a significance level of 0.05, and write a short statement that describes the results of the test.
b. Based on the outcome of the hypothesis test, which statistical error might have been committed?