Question

Table 4.1 below presents the numbers of full-time teaching staff at Canadian universities in 2019, by academic rank and by gender. Source: https://www150.statcan.gc.ca/t1/tbl1/en/cv.action?pid=3710007601

Table 4.1

Academic Rank	Females		Males	Total
Full professor	4,830		11,916	16,746
Associate professor	6,975		9,006	15,981
Assistant professor	4,290		4,362	8,652
Lecturer	2,172		1,785	3,957
Other	570		522	1,092
Total	18,837		27,591	46,428

                                                     

4.1 What is the probability that a randomly selected university teaching staff member was a female?

Fraction answer: ____________           Answer: __________ (4 decimal pl)

                                                                                                                       

4.2 What is the probability that a randomly selected university teaching staff member was a male and a full professor?                                                                                                

Fraction answer: ____________           Answer: __________ (4 decimal pl)

                                                                                                                                               

4.3 What is the probability that a randomly selected university teaching staff member was a male or an assistant professor?

                                                                                                                                   

Fraction answer: ____________           Answer: __________ (4 decimal pl)

                                                           

4.4 Given a male teaching staff member, what is the probability that this person is a lecturer?   

Fraction answer: ____________           Answer: __________ (4 decimal pl)

4.5 Is there statistical dependence between gender and academic rank based on the data in Table 4.1? Support your answer with appropriate statistical calculations.

Relevant formulas: ___________________________________________

Supporting calculations (4 decimal places): ______________________________________

Decision: ______________________

4.6 Table 4-2 below lists the approximate probabilities for different academic ranks for staff in Canadian universities and typical corresponding salaries. Source: https://www.macleans.ca/education/comparing-the-average-salaries-of-canadian-professors-in-2018/

Table 4.2

Academic Rank	Salary	Probability
Full professor	$162,000	0.3586
Associate professor	$135,000	0.3504
Assistant professor	$117,000	0.1874
Lecturer	$70,000	0.0817
Other	$52,000	0.0219

Evaluate the expected value and the standard deviation of the academic worker salaries:

Calculator functions for expected value:    __________________________

Expected value: _________________________ (to nearest $1000)

Calculator functions for standard deviation:   

Standard deviation: ______________________ (to nearest $1000)

Answer 1

We would be looking at the first 4 parts here as:

4.1) The probability that a randomly selected university teaching staff member was a female is computed here as:
= Number of females / Total staff

= 18837 / 46428

= 0.4057

Therefore 0.4057 is the required probability here.

4.2) Now the probability that a randomly selected university teaching staff member was a male and a full professor

= Total number of staff members what is a male and a full professor / Total staff

= 11,916 / 46428

= 0.2567

Therefore 0.2567 is the required probability here.

4.3) Now the probability that a randomly selected university teaching staff member was a male or an assistant professor

= ( Total number of males + Total number of assistant professor - Total number of male assistant professor ) / total staff

= (27591 + 8652 - 4362) / 46428

= 0.6867

Therefore 0.6867 is the required probability here.

4.4) Given a male teaching staff member, the probability that this person is a lecturer is computed using bayes theorem as:

= Number of male lecturer / Total number of male

= 1785 / 27591

= 0.0647

Therefore 0.0647 is the required probability here.