A researcher wishes to​ estimate, with ​90% ​confidence, the population proportion of adults who are confident with their​ country's banking system. His estimate must be accurate within 3​% of the population proportion. ​(a) No preliminary estimate is available. Find the minimum sample size needed. ​(b) Find the minimum sample size​ needed, using a prior study that found that 26​% of the respondents said they are confident with their​ country's banking system. ​(c) Compare the results from parts ​(a) and ​(b).

Astudent is determining the influence of different types of food on the growth rate of spiders. she feeds one group of spiders two caterpillars twice a week. the other group received similarly-sized beetles twice a week. she records the amount of time required for individuals to reach sexual maturity. her hypothesis is that the spiders feeding on caterpillars will have a faster growth rate because caterpillars have a higher protein content compared to beetles. in this experiment, what is the dependent variable? spiders assigned to different feeding groups. time required to reach sexual maturity number of prey items fed twice a week. growth rates of each group.