Do (0,1) and r+ = (0,[infinity]) have the same cardinality? if so, either give an explicit bijection (and prove that it is a bijection) or provide an injection from (0,1) to (0,[infinity]) and an injection from (0,[infinity]) to (0,1) (so that by cantor-bernstein theorem the two sets will have the same cardinality). if not, then prove that they have different cardinalities

According to a study conducted in 2015, 18% of shoppers said that they prefer to buy generic instead of name-brand products. suppose that in a recent sample of 1500 shoppers, 315 stated that they prefer to buy generic instead of name-brand products. at a 5% significance level, can you conclude that the proportion of all shoppers who currently prefer to buy generic instead of name-brand products is higher than .18? use both the p-value and the critical-value approaches.