In: Statistics and Probability
            A comparison of salaries at comparable institutions in two
states was undertaken to examine if states...
                
            
- A comparison of salaries at comparable institutions in two
states was undertaken to examine if states pay professors
similarly. Professors in each institution were selected and then
matched on the basis of gender, length of service with the
institution, number of publications, number of grants obtained, and
average student evaluations.  The data are as
follows.
 
            Pair     State
"T"       State
"G"                   Pair     State
"T"       State
"G"       
            1          38,432             42,134                         6          39,232             42,143
            2          47,984             49,243                         7          48,394             50,003
            3          58,423             63,243                         8          51,248             53,381
            4          35,345             36,454                         9          64,458             68,454
            5          43,214             44,365                         10        42,345             43,294
                        
- What is the null hypothesis?
 
- What is the alternative hypothesis?
 
- What test statistic will you use? Why?
 
- What alpha level will you set?
 
- What is the average salary for each state?
 
- What is the value of the test statistic?
 
- What is the p-value?
 
- What is your decision about the null hypothesis?
 
- What is your interpretation of the results? (2-3 sentences;
2pts).