Breast Cancer Wisconsin Diagnostic dataset is a classic dataset where interactive image processing techniques, along with a linear$-$programming$-$based inductive classifier, was used to create a highly accurate system for diagnosis of breast tumors $($W$.$ Street, W$.$ Wolberg, O$.$ Mangasarian, $1993).$

Information on various features were computationally extracted from digital images of fine needle aspirate biopsy slides. Features correspond to properties of cell nuclei, such as size, shape and regularity. The mean, standard error, and worst value of each of $10$ nuclear parameters is reported for a total of $30$ features.

The dataset brca.csv has information on $30$ features and diagnosis status $[$outcome variable y which is a factor with two levels denoting whether a mass is malignant $($M$)$ or benign $($B$).]$

Consider the mean and worst values of radius of cell nuclei. Using a suitable approach demonstrate the sampling distributions of the difference of sample means of mean values and of the difference of sample means of worst values of radius for the malignant and benign group. How do these two sampling distributions compare?

Repeat the above steps to demonstrate the sampling distributions of the difference of sample means of mean values and of the difference of sample means of worst values of perimeter for the malignant and benign group.

How do the sampling distribution of mean values compare with that of the worst values?