DATA DESCRIPTION

(A FICTITIOUS DATASET DESIGNED FOR THE ASSIGNMENT ONLY)

A consulting firm randomly selected 150 young employees in Tasmania. These selected employees

answered questions and undertook a standard IQ test and a KW test. The KW test examines

respondents' knowledge about the duties in their workplaces and the knowledge about the Australian

and Tasmanian labour markets. Respondents' answers are entered a spreadsheet where each column

represents a variable. These variables include:

1. wage: monthly earnings in dollars

2. hours: average weekly working hours

3. IQ: IQ score

4. KW: knowledge of work score

5. educ: years of education

6. exper: years of work experience

7. tenure: years with the current employer

8. age: age in years

9. marriage: marriage status

10. gender: female or male

11. urban: =Y if lives in urban areas

=N if lives in rural areas

12. sibs: the number of siblings

13. brthord: birth order, e.g. =2 means he/she is the second child in the family.

14. meduc: mother's education

15. feduc: father's education

The missing values are shown by a "." in the cells.

Questions:

1. Read the provided raw data carefully to check whether all respondents have provided

information for each variable. Explain what you have done to manage the missing data. Clearly

indicate the final number of observations (respondents) you will use in the following analysis.

Submit an electronic copy of the Excel spreadsheet of the final dataset together with your

assignment. All your following analysis should be based on this final dataset.

[10 marks]

2. Pick up two numerical variables and two categorical variables and then describe each of them

one by one. Use appropriate tables/graphs and numerical measures to help you describe the

distribution of the variables.

[10 marks]

3. It's often asked what factors relate to IQ score and KW score. Look through your data and

first pick up one numerical variable that you think may relate to IQ score. Explain why you

pick up this variable. Then use an appropriate graph and an appropriate numerical measure to

discuss the empirical relationship between IQ score and this numerical variable. Repeat the

same exercise for the relationship between KW score and a numerical variable to which you

think KWmay relate.

[15 marks]

4. You want to look at the relationship between gender and wages. However, you notice that

gender is a categorical variable and wage is a numerical variable. One way to work on two

different types of variables is to transform one variable to the type of the other. You decide

to generate a categorical variable based on the level of wage, and this categorical variable has

two values, "high" and "low". For example, you choose a threshold value for wage, and if a

respondent's wage is no less than the threshold value, you enter "high" and enter "low"

otherwise.

a. Describe in detail how you have decided the threshold value for generating the new

categorical variable for the level of wage. Then use an appropriate graph to present this

variable. (Hint: you may choose to use an appropriate numerical measure of wage as the

threshold value).

b. Present these two categorical variables together using an appropriate graph, and then

discuss what the graph shows.

[4 marks]

c. Produce a contingency table to present these two categorical variables. Based on the

contingency table, calculate the related (empirical) joint and marginal probabilities. You

may find helpful to produce another contingency table to show your calculated

probabilities. (Hint: you may need Excel skills -- e.g. use the commands such as "sort" or

"countif" to count the relevant frequencies, or use PivotTable function)

[8 marks]

d. Based on the sample information, calculate the probability of either being a female or

getting a low wage level, and calculate the probability of being a female conditional on

getting a low wage level

[5 marks]

e. Examine whether the statement "Males tend to receive high wages than females" is true,

false or inconlusive based on the sample information. Explain your response.

[5 marks]

[Total Marks 28]

5. Suppose that the population average of (monthly) wage of young employees in Tasmania in

the previous year before this survey was conducted was $900.

f. Conduct a hypothesis test that the population average wage of young employees in

Tasmania during the year of survey remains the same as in the previous year.

[7 marks]

g. Construct a 95% confidence estimate for the population average wage, and comment

whether the population average wage in the year of survey remains the same as in the

previous year.

6. You want to use the collected data to study what is the most important factor that affects

young employees wage in Tasmania. Use simple regression analysis to answer the following

questions. (For each regression you run, show the Excel regression output and report the

regression equation. Partial marks from the following questions assign to your regression

results.).

a. Do the years of education have significant impact on the wages? (You need to explain the

choice of the null and the alternative hypotheses.)

[5 marks]

b. Do the IQ scores have significant impact on the wages? (You need to explain the choice

of the null and the alternative hypotheses.)

[5 marks]

c. Which of the two variables is a better predictor for the wage, years of education or IQ

scores? Explain why.

[3 marks]

d. Do the years of work experience have significant impact on the wages? (You need to

explain the choice of the null and the alternative hypotheses.

[3 marks]

e. Do the KW scores have significant impact on the wages? (You need to explain the choice

of the null and the alternative hypotheses.)

[3 marks]

f. Which of the two variables is a better predictor for the wages, years of work experience or

KW scores? Explain why.

[3 marks]

g. Newspapers often criticize a weak link between wage and education comparing with the

link between wage and work experience. Discuss if the criticism is consistent with our data

xl data