STATS 371-Most penguin species are not sexually dimorphic

Subject: Mathematics    / Statistics
Question

Q:1Most penguin species are not sexually dimorphic, which means that there are no obvious outward body characteristics which indicate gender. Therefore, penguin gender must be determined by a blood test. A penguin researcher is interested in estimating the proportion of females in a large penguin population. She takes a random sample of n = 20 penguins, and determines the gender of each one using a blood test. She finds 12 males and 8 females. Let ? be the proportion of females in the population.

Q:2A university is conducting a survey in order to estimate the results of an upcoming local election. They intend to take a simple random sample of individuals from the population of eligible voters. Each selected individual will be asked whether they will vote for Candidate A, yes or no. The university intends to use the results to create a 95% CI for the population proportion of voters who will vote for Candidate A. They desire the interval to have a half-width of no more than 0.03. How many individuals must they sample? (Hint: the half-width of a CI for a population proportion is maximized when the sample proportion is set to p = 0.5.)