Please show work for each question

1. (20pt) A researcher is interested in the effects of racism on birth weight. He constructs a dataset containing the birth weight of African American children (in pounds) and their mothers' self-reported experience with racism during their pregnancy. He divides the children into two groups-those whose mothers reported experiencing no race-related incidents and those whose mothers reported at least one experience of racism during their pregnancy. Assuming birth rates to be normally distributed, test the null hypothesis of no difference in mean birth weight between the two groups.