Hi, need help with the following question, Topic: Hypothesis Testing, Comparing Two Population Means

A researcher wants to perform a hypothesis test to see if the mean salary of the faculty in private and public institutions are different. Random samples of 36 faculty from private and public institutions were selected. Salaries of the selected faculty from private and public institutions are provided to you infacultysalary.csvDownload facultysalary.csvfile.

1. Calculate the descriptive statistics: mean, standard deviation for the two samples
2. When carrying out a hypothesis test to achieve the aforementioned goal, would you recommend using pooled variance approach or unpooled variance approach? Provide reasoning for your choice.
3. Carry out the hypothesis test using unplooled variance approach. Clearly define the parameters and show all your work for 6-steps. get the final test statistic and the p value. However, you need to show all the mathematical work to get to the final answer.
4. Now, re-do everything you did in part 5, using pooled variance approach.
5. Compare the test statistics and p values you obtain in parts 5 (unpooled variance) and 6 (pooled variance). Clearly write your observations.

Faculty Salary

private	public
103.1	54.5
82.1	96
139.8	43.1
82.7	98.4
91.1	122.6
61.3	66.6
65.1	56
151.3	124.4
112.7	54.8
83.1	86.3
71.5	55.8
65.9	115.7
70.5	99.6
83.3	82.6
97.2	76.4
98.6	40.2
91.8	44.7
88.7	72.5
64.3	80
90.5	75.1
117.5	110.6
66.2	93.9
65	115
122.1	98.3
109.6	102.5
101.2	36.4
100.8	81.9
107.5	101.1
109.7	72.2
129.1	57.7
120.4	104.8
104.3	75.7
141	85
127.6	76.1
47.8	82.6
101.9	100.1