As a student of ECON1005 suppose you were asked to assist a

As a student of ECON1005, suppose you were asked to assist a co-worker in investigating whether there is an association between gender and annual salary of researchers in your country. Data was gathered from researchers in your country in your country. MINITAB was used to generate stem-and-leaf diagrams for the salaries of both the female and male researchers. See Exhibit 1 below.

Exhibit 1

Stem-and-Leaf Display: Salary Female, Salary Male

Stem-and-leaf of Salary Male N = 20

Leaf Unit = 1000.0

1   5   8

2   6   4

7   7   57789

(4) 8   3377

9   9   044677

3   10 034

Stem-and-leaf of Salary Female N = 15

Leaf Unit = 1000.0

1   5 8

5   6 1345

(3) 7 148

7   8 389

4   9 2245

(a)Calculate the mean salary for both the female and the male researchers. All relevant working must be clearly shown.

(b)Calculate the standard deviation of the salaries for both the female and the male researchers. All relevant working must be clearly shown.

(c)Comment on your answers for parts (c) and (d), in relation to the purpose of your study, that is, the association between gender and annual salary of researchers in your country.

MINITAB was used to generate box-and-whisker diagrams for the salaries of both the female and male researchers. See Exhibit 2 below.

Exhibit 2

(d)With reference to the box-and-whisker diagrams, compare the salaries of the researchers selected in your sample, by gender. Ensure that you comment on the skewness, the median, the interquartile range, the minimum and the maximum values of both diagrams.

MINITAB was used to generate the descriptive statistics for all the 35 researchers selected in the sample. See Exhibit 3 below.

Exhibit 3

Descriptive Statistics: ResearcherSalary

Variable   N N*   Mean SE Mean TrMean StDev Minimum     Q1 Median     Q3

Salary    35   0 82951     2266   83200 13404    58100 74800   83800 94300

Variable Maximum

Salary     104500

(e)What does TrMean represent? Comment on the value of the TrMean and show how this value was calculated.

(f)For further analysis, a table is drawn showing the number of females and the number of males whose salaries were below the median salary and equal to or above the median salary. Complete the table below:

Salary < $83800

Salary ³ $83800

Total

Female

Male

Total

35

(g)Using your table in part (h), determine the probability that a randomly selected researcher from your sample, is a female OR has a salary < $83800.

(h)Using your table in part (h), determine the probability that a randomly selected researcher from your sample, is a female AND has a salary < $83800.

(i)Given that a randomly selected researcher from your sample is a female, what is the probability that her annual salary is < $83800?

(j)Are the events “female researcher” and “salary < $83800” mutually independent events? Support your answer with relevant calculations or explanations.

Solution