Answer:
Following are the responses to the given question:
Step-by-step explanation:
For point a:
In R-Studio, we first insert the data set,
Please notice that perhaps the blue colored lines are input and the green lines are R-Studio results.
![Class \ 1 = c(72,73,74,75,76,79,82,83,84,86,91,92,93,93,94,95,95,97,98,98)\\\\Class\ 2 = c(59,65,68,68,69,72,73,78,80,82,82,83,83,85,88,88,89,94,96,97,98)](https://tex.z-dn.net/?f=Class%20%5C%201%20%3D%20c%2872%2C73%2C74%2C75%2C76%2C79%2C82%2C83%2C84%2C86%2C91%2C92%2C93%2C93%2C94%2C95%2C95%2C97%2C98%2C98%29%5C%5C%5C%5CClass%5C%202%20%3D%20c%2859%2C65%2C68%2C68%2C69%2C72%2C73%2C78%2C80%2C82%2C82%2C83%2C83%2C85%2C88%2C88%2C89%2C94%2C96%2C97%2C98%29)
We will get the smallest observation, first, mid, third, and largest quartile for both classes and use a summary of 5 numbers,
![\to five\ num(Class\ 1) \\\\\[1\] \ 72.0 77.5 88.5 94.5 98.0 \\\\\to five\ num(Class\ 2) \\\\\[1\]\ 59 72 82 88 98](https://tex.z-dn.net/?f=%5Cto%20five%5C%20num%28Class%5C%201%29%20%5C%5C%5C%5C%5C%5B1%5C%5D%20%5C%2072.0%2077.5%2088.5%2094.5%2098.0%20%5C%5C%5C%5C%5Cto%20five%5C%20num%28Class%5C%202%29%20%5C%5C%5C%5C%5C%5B1%5C%5D%5C%20%2059%2072%2082%2088%2098)
The table can be defined as follows:
![Class\ 1\ \ \ \ \ \ \ \ \ \ \ \ Class\ 2 \\](https://tex.z-dn.net/?f=Class%5C%201%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%09Class%5C%202%20%5C%5C)
![Smallest \ value\ \ \ \ \ \ \ 72\ \ \ \ \ \ \ 59\\First \ quartile \ Q1\ \ \ \ \ \ \ 77.5\ \ \ \ \ \ \ 72\\Median\ Q2 \ \ \ \ \ \ \ 88.5\ \ \ \ \ \ \ 82\\Third \ quartile \ Q3 \ \ \ \ \ \ \ 94.5\ \ \ \ \ \ \ 88\\Largest \ value \ \ \ \ \ \ \ 98\ \ \ \ \ \ \ 98\\](https://tex.z-dn.net/?f=Smallest%20%5C%20value%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%0972%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%0959%5C%5CFirst%20%5C%20quartile%20%5C%20Q1%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%0977.5%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%0972%5C%5CMedian%5C%20%20Q2%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%0988.5%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%0982%5C%5CThird%20%5C%20quartile%20%5C%20Q3%09%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%2094.5%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%0988%5C%5CLargest%20%5C%20value%09%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%2098%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%0998%5C%5C)
The parallel boxplots in R-Studio as,
Please find the graph file.
For point b:
Its performance overall of Class 1 is better, while the median of class 1 is greater than class 2, as well as the value (grades) of class 1, is less dispersed in relation to class 2.
For point c:
The stated 90 percent confidence interval for a significant difference is (0.09299, 11.413) Users now calculate the difference among Class 1 and Class 2 plan presented of mean value as:
![mean \ (Class \ 1) \\\\\[1\]\ 86.5\\\\mean\ (Class\ 2)\\\\](https://tex.z-dn.net/?f=mean%20%5C%20%28Class%20%5C%201%29%20%5C%5C%5C%5C%5C%5B1%5C%5D%5C%2086.5%5C%5C%5C%5Cmean%5C%20%28Class%5C%202%29%5C%5C%5C%5C)
![\[ 1 \] \ 80.80952\\\\Difference = 86.5 - 80.80952 = 5.69048](https://tex.z-dn.net/?f=%5C%5B%201%20%5C%5D%20%5C%2080.80952%5C%5C%5C%5CDifference%20%3D%2086.5%20-%2080.80952%20%3D%205.69048)
Its discrepancy among two estimations is between confidence interval of 90 percent (0.09299, 11.413). Its mean population of grades of two classes therefore differs significantly.