Using R to solve following questions: Using the file "PHD. The csv file has the following columns: (Download PHD.csv from here https://drive.google.

Using R to solve following questions:

Using the file "PHD.csv". The csv file has the following columns: (Download PHD.csv from here https://drive.google.com/file/d/1nAX9L9OxOulIEnF59kjzBQQT0MKJsMN3/view?usp=sharing)

Column 1.

Year: How many years it took the candidate to graduate with a Ph.D

Column 2.

Uni: Which university the subject studied at (Berkeley, Columbia, Princeton).

Column 3.

Res: Residency of subject (permanent, temporary)

Problem I:

(a) Find the average years to graduation for the three

schools. Which school had the highest average?

(b) Find the standard deviation of years to graduation

for the three schools. Which school had the lowest

deviation from the mean?

(c) Did temporary or permanent residents take longer

to graduate on average? Justify your answer.

(d) Find the five number summary of the number of

years it took to graduate. Do you believe the mini-

mum is an outlier? Justify your answer.

Problem II. Continue with the "PHD.csv" dataset.

(a) Generate boxplot of years it took for the subjects

to graduate by residency. Do you believe there is a

significant difference between the groups? Explain.

(b) Generate histogram of years to graduate by school

Which year had the most subjects in it for Prince-

ton?

(c) Generate mosaic plot of residency and school.

Grouping by school, who had the highest proportion

of temporary residents?

(d) Generate mosaic plot of residency and school.

Grouping by residency, who had the highest probability

of going to Berkeley?

Probkem III. Continue with the "PHD.csv" dataset. For the following

problems, you must show results from either a plot, a table,

or an aggregate command to back up your answers.

(a) How may subjects were there attending Columbia?

(b) How different was each schools average time to graduate

compared to the overall average?

c) Were there more people who attended Berkeley

and were temporary residents, or who attended

Columbia and were temporary residents (looking at

1. the absolute magnitude).

(d) If you were told a subject came from Princeton and

was a temporary resident, what would you estimate

their years to graduate to be (based on only summary statistics and plots)?

Download PHD.csv from here https://drive.google.com/file/d/1nAX9L9OxOulIEnF59kjzBQQT0MKJsMN3/view?usp=sharing