The starting salary is one important factor to compare employability across universities. A simple random sample of 35 students from the University of M records their average starting annual salaries. The sample mean is $67.6K and the sample standard deviation is $12.3K. Another simple random sample of 54 students from the University of S report that their average starting annual salary is $65.7K with a sample standard deviation of $11.4K. ($1K mean 1000 dollars)

What is the total number of observations in this data set?

Use the information provided from the previous question to carry out a test to investigate whether the mean starting salary for students from the University of M is higher than from the University of S at 10% significance level.

Specifically, you must

(a) define any new notation, (b) briefly justify your testing procedure, (c) state the hypotheses, (d) calculate the test statistic and show your calculation steps, (e) use the p-value approach, (f) make decision for the test and briefly explain.