1. Import the "reacttimes" data set and consider the 50 observations of the variable "Times" to be a sample from a larger population. Find a 96% confidence interval for the population mean. Construct a normal quantile plot and comment on the appropriateness of the procedure. Hint: reacttimes <- read.table("https://www.math.uh.edu/~wwang/MATH3339/dataset/reacttimes.txt",header = T) t.test(reacttimes$Times,conf.level = 0.96) qqnorm(reacttimes$Times) qqline(reacttimes$Times).
2. We wish to estimate the population mean of a variable that has standard deviation 70.5. We want to estimate it with an error no greater than 6 units with probability 0.99. How big a sample should we take from the population? What happens if the standard deviation and the margin of error are both doubled?
3. The FDA sampled 60 boxes of cereal and found 10 with insect parts. Find a 95% confidence interval for the true proportion of cereal boxes with insect parts. Use R to answer this question. Hint: prop.test(n,x,correct=F)