a 2011 study reported that the proportion of women in the southern us who experienced early menopause (menopause before age 43) was significantly different from the proportion in the northeast: 18.9% in the south compared to 12.3% in the northeast. another group of researchers wants to explore regional differences in age at early menopause ten years later, since overall age at menopause appears to be increasing among us women. how many women from the south and northeast, respectively, must the researchers include to generate a 95% confidence interval for the difference in proportions with a margin or error not exceeding 5%?