Question

1. Using R Studio: Include R Code: The following data is from IQ tests for pairs of twins that were separated at birth. One twin was raised by the biological parents, the other by adoptive parents.

Foster:     80, 88, 75, 113, 95, 82, 97, 94, 132, 108

Biological:            90, 91, 79, 97, 97, 82, 87, 94, 131, 115

Find a 90% confidence interval for the differences of mean. What do you assume about the data? In particular, are the two samples independent?

Answer 1

The R code for the paired T-test is given below:

X1 <- c(80, 88, 75, 113, 95, 82, 97, 94, 132, 108)
X2 <- c(90, 91, 79, 97, 97, 82, 87, 94, 131, 115)
t.test(X1, X2,
alternative = "two.sided",mu = 0, paired = TRUE, var.equal = FALSE,
conf.level = 0.90)

The putput is

data: X1 and X2
t = 0.041019, df = 9, p-value = 0.9682
alternative hypothesis: true difference in means is not equal to 0
90 percent confidence interval:
-4.368937 4.568937
sample estimates:
mean of the differences
0.1

The 90% confidence interval for the difference in means is:

Since this is a paired test, the two samples are not independent.