# Page 1 #Exercise 1. Suppose I picked out a sample of 25 M&M's where 11 were blue. #Exercise 2. p^hat = 11/25 in my case #Exercise 3. Other people in the room all had values between about 10/25 and 18/25 #Question 1. It is very unlikely that a small sample will give a proportion that is /exactly/ equal. #Question 2. We should give some range which we think the true proportion lies with, e.g. between 10/25 and 18/25. #Page 2 #Question 1. (Go to http://www.rossmanchance.com/applets/OneProp/OneProp.htm?candy=2) #Question 2. (Go to http://www.rossmanchance.com/applets/OneProp/OneProp.htm?candy=2) #Page 3 #Question 3. (Go to http://www.rossmanchance.com/applets/OneProp/OneProp.htm?candy=2) #Question 4. ME should be approximately equal to 0.45*(p^), such that the interval ((p^) - ME, (p^) + ME) will contain tru value of p = 0.5 #ME Excersice 2. Increasing the sample size reduces the margin of error. #Confidence Interval Excersice 1. #Question 1. Zc = 1.96 #Question 2. ME for 95% confidence level n <- 25 p <- 13/25 Zc <- 1.96 ME <- Zc*(sqrt((p*(1-p))/n)) print(paste("ME = ", ME)) #Question 3. To calculate confidence interval print("((p^) - ME ,(p^) + ME)") print(paste("(", p-ME, " , ",p+ME ,")")) #Page 4 #Question 4. Yess. Confidence interval contains the true value of p = 0.5 #Question 5. 95% #Confidence Interval Excersice 2. #Question 1. (Go to http://rossmanchance.com/applets/ConfSim.html) #Question 2. (Go to http://rossmanchance.com/applets/ConfSim.html) #Question 3. 93,94,96,98 percent #Question 4. After repeating step 3 multiple times, around 2 to 7 percent of intevals do not contains true value of p = 0.5 #Question 5. 90% confidence interval are narrower than 95%. 81 to 95 percent intervals contains true value of p = 0.5 #Question 6. Confidence interval width and confidence level are inversely related. #Confidence Interval Excersice 3. #Question 1. prop.test() #Question 2. test <- prop.test(13,25, conf.level = 0.95) print(test) #Question 3. print("Manually calculated confidence interval") print(paste("(", p-ME, " , ",p+ME ,")")) print("Confidence interval calculated using R") print(test$conf.int) #Page 5 setwd("~/bd4isu/") data <- read.csv("national_longitudinal_wt_ht_gender.csv") #For male height t.test(data[data$Gender == 'M',2], conf.level = 0.95) #For male weight t.test(data[data$Gender == 'M',3], conf.level = 0.95) #For female height t.test(data[data$Gender == 'F',2], conf.level = 0.95)