# Question 2 # The state of Florida is in the midst of a homeowners insurance crisis,...
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# Question 2 # The state of Florida is in the midst of a homeowners insurance crisis, with # insurance costs skyrocketing and pricing many homeowners out of the market. # More and more homeowners are resorting to self-insurance, saving money that # would be spent on insurance in the hopes that the savings can cover any issues # that arise that would normally fall under an insurance policy. (Some people # might call this `not having insurance', but sure, let's # go with `self-insurance'.) # A survey of 487 Florida homeowners found that 82 of those surveyed # reported relying on self-insurance. # Question 2.a # Based on the sample proportion found, what is the estimated standard error # of the distribution of phat? # Save your answer in the variable q2.a q2.a<-sqrt((0.168 * (1 - 0.168)) / 487) # Question 2.b # Calculate a 90% confidence interval for the true proportion of Florida # homeowners who rely on self-insurance. (Your answer should be formatted # similarly to the function output, if done by hand). # Save your answer in the variable q2.b q2.b<-ci.for.proportion(0.168, 487, 0.90) # Question 2.c # If the true proportion of Florida homeowners relying on self-insurance were # p=.177, what is the true standard error of the distribution of phat? # Save your answer in the variable q2.c q2.c<-sqrt(0.177 * (1 - 0.177) / 487) # Question 2.d # If the true proportion of Florida homeowners relying on self-insurance were # p=.177, what is the probability that the interval you found in q2.b # contains the true proportion? # Save your answer in the variable q2.d q2.d<-0.90 # Question 2.e # If the true proportion of Florida homeowners relying on self-insurance were # p=.202, what is the true standard error of the distribution of phat? # Save your answer in the variable q2.e q2.e<- sqrt((0.202 * (1 - 0.202)) / 487) # Question 2.f # If the true proportion of Florida homeowners relying on self-insurance were # p=.202, what is the probability a 95% interval constructed from the sample # used in q2.b would contains the true proportion? # Save your answer in the variable q2.f q2.f<-ci.for.proportion(0.202, 487, 0.95) # Question 2.g # If the true proportion of Florida homeowners relying on self-insurance were # p=.202, what is the probability a 95% interval constructed from a new sample # of size 487 would contains the true proportion? # Save your answer in the variable q2.g q2.g<- ci.for.proportion(0.202, 487, 0.95) # Question 3 #A 2022 survey of high school students found that a reported 14.1% of students used e-cigarettes. Researchers #attempting to show that the proportion of students using e-cigarettes has decreased in 2023. They take a sample of #189 high school students and find that 19 of the high school students used e-cigarettes. #Researchers use this sample to conduct a hypothesis test to determine if there is evidence that less students are #using e-cigarettes than the previous year. They plan to test their hypothesis at the = 5% level. #Your answers should be exact, utilizing the binomial distribution.