As discussed previously, Manager One seems to perform particularly well, whereas Manager Two has poor performance.

> apply(fund.mini, 2, mean)
Manager1 Manager2 Manager3 Manager4 Manager5 
     3.0     -0.1      2.8      0.5      0.3 

Is there evidence of a meaningful difference in performance between these two managers? Performing a paired t-test using the t.test() function repaired results in a p-value of \(0.038\), suggesting a statistically significant difference.

> t.test(fund.mini[, 1], fund.mini[, 2], paired = T)
	Paired t-test
data:  fund.mini[, 1] and fund.mini[, 2]
t = 2.128, df = 49, p-value = 0.03839
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 0.1725378 6.0274622
sample estimates:
mean of the differences 
                    3.1 

Question

• MC1: Use a paired t-test to determine whether there exists a significant difference (\(p < 0.05\)) between the performance of manager 3 and 4. Which Statement is correct?
  1. The difference between manager 3 and 4 is not statistically significant
  2. The difference between manager 3 and 4 is statistically significant

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Assume that:

• The ISLR2 library has been loaded
• The Fund dataset has been loaded and attached