In a prospective cohort study, 20 patients with alopecia (hair loss) had platelet-rich plasma (PRP) injected in their scalps. After three months, the mean difference in hair density (after - before) was 170.70 hairs per square centimeter with a standard deviation of 37.81 hairs>cm². 

(a) What does it mean for this study to be a prospective cohort study?
(b) What is the variable of interest in this study? Is it qualitative or quantitative?
(c) State the null and alternative hypotheses to determine if hair density increased.
(d) The researchers indicated that a test for normality indicated it was reasonable to conclude the change in hair density is approximately normal with no outliers. Does the evidence suggest that PRP injected in the scalp increases hair density? Use an a = 0.05 level of significance.
(e) How would the alternative hypothesis change if the differences were computed “before-after”?