The Human Papillomavirus (HPV) is linked to certain reproductive cancers and is the most common sexually-transmitted infection (CDC). Vaccinating young teens can significantly reduce the spread of HPV and reduce cancers and other diseases linked to HPV. It is recommended that girls and boys are vaccinated, but most publicity about the vaccine focuses on women. So let's consider data from the US on the percentage of males and females who have received the full 3-shot round of the HPV vaccine.
23 states were sampled to determine the percentage of females, age 13-17 that had completed the full HPV vaccine. The mean percentage for females was 73.64%, with a standard deviation of 8.86%. A comparable sample of 31 states found that the mean percentage for males was 56.42%, with a standard deviation of 10.28%. Assume the samples are independent. (Do NOT change the percentages to decimals - just work with the numbers as they are.)
a. At the 0.10 significance level, is there a difference in the variability of the vaccination rates between males and females?
b. Given the result from part (a) about the variances, test whether more women are vaccinated, on average, than men. Use a 0.01 significance level. (If you need it, the degrees of freedom are 50.)