Hypothesis testing - Paired sample t test or two sample t test I'm trying to test the hypothesis that there is a significant difference between the data below. I'm having trouble deciding whether I should use a paired sample t test or a 2 sample t test. Can't decide whether they're 2 independent groups or paired. The sentence **"In the 1990’s a group of researchers reported the results of a study that controlled for genetic and socioeconomic differences by examining 15 pairs of monozygotic twins..."** is making me lean towards using a paired t test. Although I'm still quite unsure. ![enter image description here](

I personally would use a paired $t$-test here: there is an obvious pairing here (twins: one unaffected, the other affected), and the samples are obviously very dependent (twins).

Remember that the two-sample $t$-test assumes that your two samples are **independent**.

Demonstration in R, in case you would like the code for $H_1$ with $\mu_{\text{unaffected}}-\mu_{\text{affected}} \
eq 0$:


unaffected <- c(1.94, 1.44, 1.56, 1.58, 2.06, 1.66, 1.75, 1.77, 1.78, 1.92, 1.25, 1.93,
2.04, 1.62, 2.08)
affected <- c(1.27, 1.63, 1.47, 1.39, 1.93, 1.26, 1.71, 1.67, 1.28, 1.85, 1.02, 1.34,
2.02, 1.59, 1.97)

difference <- unaffected - affected

t.test(difference)

One Sample t-test

data: difference
t = 3.2289, df = 14, p-value = 0.006062
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
0.0667041 0.3306292
sample estimates:
mean of x
0.1986667