Bootstrap Method Practice

Example: Correlation between spouses ages

marriages = read.csv("http://people.hsc.edu/faculty-staff/blins/StatsExamples/marriageAges.txt")
head(marriages)

##   husb wife
## 1   25   22
## 2   25   32
## 3   51   50
## 4   25   25
## 5   38   33
## 6   30   27

The data frame marriages contains data from 24 couples that were married in Cumberland county Pennsylvania one month. Assume for now that these couples are representative of couples throughout the United States.

1. Use the plot() function to make a scatterplot that shows the correlation between the ages of husbands and wives.

2. Find the correlation using the cor() function.

3. Of course, the correlation you found is a sample statistic, not the true population parameter for all married couples in the United States. Make a bootstrap distribution for the correlation. In order to make a bootstrap distribution, you need to be able to create a boostrap sample from the rows of a data frame. Here is one way to do this in R:

   n <- nrow(marriages)
   random.rows <- sample(c(1:n), n, replace = T)
   boot.sample <- marriages[random.rows, ]

4. Using the bootstrap percentile method, find a 95% confidence interval for the correlation between the ages of husbands and wives in the United States.