This is our sample questions for final exam, we don't need to upload it as our homework cuz lecturer has finished it. BUT I'm still confusing about this two questions, could you tell me the THEORY that each question investigated? U don't need to calculate just explain. Thank u so much.

Background of Data In this exam, you will look at some analysis on a Technology company employee and their experience, education and their annual salary. In addition, the company examines various departments and their relationship with the employee profiles. The data is based on the records from 2003 to 2010. You are required to examine the outputs covering different areas of the analysis and provide the insight report for the company to understand its departmental roles and their driving capacity towards the future expansion in the country.

The company would like to find more details about the departments and the respective employees. One of the departments to look into is the production and engineering and its number of employees by gender and their educational attainment.

(a). To do so the data is summarised int the contingency (pivot) tables. Shown below is the table illustrating the number of employees from all the departments by gender and the educational attainment (in years).

Department (All)

Count of Employee Gender

Education Female Male Grand Total

0 8 2 10

2 10 9 19

4 69 46 115

6 27 24 51

8 5 4 9

Grand Total 119 85 204

Next is a table showing the employees from the Production and Engineering by gender and the educational level.

Department Production and Engineering

Count of

Employee Gender

Education Female Male Grand Total

0 4 1 5

2 3 1 4

4 27 22 49

6 8 9 17

8 1 2 3

Grand Total 43 35 78

i. From the above two pivot tables, calculate the rate of the employees in the production and engineering who have six years of educational attainment and are males. Show all workings.

ii. Calculate the production and engineering department rate of the employees of this technology company. Show all workings. (2 marks)

iii. Discuss how the probabilities vary with the years of education attainment and the gender given that the employees are from the department of production and engineering (Dept P&E). (4 marks)

The table below is for the employees that are in the department of production and engineering.

Department Production and Engineering

Count of Employee Gender

Education Female Male Grand Total

0 5.13% 1.28% 6.41%

2 3.85% 1.28% 5.13%

4 34.62% 28.21% 62.82%

6 10.26% 11.54% 21.79%

8 1.28% 2.56% 3.85%

Grand Total 55.13% 44.87% 100.00%

iv. From the above table, what does the value 21.79% mean?

v. If an employee is randomly selected, what is the probability that he or she is a female and has attained four years of education given the employee is from the department of production and engineering? Show all working. (1 mark)

vi. What is the proportion of a randomly selected employee who is from the department of production and engineering has less than four years of education and is a male? Show all working. (2 marks)

(b). Looking at the table below answer the following questions

Department Production and Engineering

Count of Employee Gender

Education Female Male Grand Total

0 80.00% 20.00% 100.00%

2 75.00% 25.00% 100.00%

4 55.10% 44.90% 100.00%

6 47.06% 52.94% 100.00%

8 33.33% 66.67% 100.00%

Grand Total 55.13% 44.87% 100.00%

i. From the above table, what is the meaning of the 33.33%? (1 mark)

ii. From the above table, explain how the value in part (i) above was calculated? (1 mark)

iii. The company manager is interested to find whether the years of educational attainment is independent of whether you are male or female. Use the data in the pivot table above. If these two variables were independent then write down a probability statement that you would expect to hold. (2 marks)

iv. Use data from the pivot table above to show that gender and the years of education are NOT independent. (2 marks

Question 3 (20 marks)

(a). The following table shows trends in the composition of employees of the computer Technology Company over the 8 year period since 2003. Specifically, it contains the number of employees age. Use this information to answer the following questions.

Year Time (year) Number of employees aged 40 and over Total number of employees % of employees aged 40 and over

2003 1 6 15 40.00%

2004 2 10 35 28.57%

2005 3 22 56 39.29%

2006 4 31 51 60.78%

2007 5 14 22 63.64%

2008 6 8 15 53.33%

2009 7 8 8 100.00%

2010 8 2 2 100.00%

i. If you were to calculate the average annual rate at which the company employed the staff for the entire 8 year period, show how you would do that. (2 marks)

ii. It would be a good idea to compute the yearly percentages of employees in the company in order to understand some statistical insights. What has been calculated in the table is the percentages of the employees who are 40 years old and over. As an example, calculate the proportions of the employees who are less than 40 years old in 2006 and 2007. (1 mark

(b). The company would like investigate further the claim that the company has stopped recruiting older people and so the number of employees who are 40 years and over is decreasing after a few years after it started. To investigate this claim, a statistician estimated a regression model with a linear time trend in "Time (Year)" with the dependent variable being "% of employees aged 40 years and over" and the results are given below:

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.890708

R Square 0.793360

Adjusted R Square 0.758921

Standard Error 0.132156

Observations 8 ANOVA

df SS MS F Significance F

Regression 1 0.4023277 0.4023277 23.0360710 0.0030020

Residual 6 0.1047907 0.0174651

Total 7 0.5071184

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 0.166583 0.102975 1.617706 0.156853 -0.085387 0.418553

Time (year) 0.097874 0.020392 4.799591 0.003002 0.047976 0.147771

i. Is it a mistake that in the above regression model we did not include a seasonal dummy variable(s). Give reasons. (2 marks)

ii. State and give interpretation of the coefficient for the intercept in this regression model and discuss whether it is meaningful. (2 marks

iii. State and interpret the coefficient for Time (Year) in this regression model. Is the sign consistent with the claim in the question? (2 marks)

iv. Carry out a hypothesis test at the 5% significance level of whether there has been a change in the proportion of company employees who are aged 40 years and over during the 8 years. (4 marks)

v. Would your conclusion have differed if you had chosen a 0.1% significance level? (2 marks)

vi. Calculate the predicted value for the proportion of employees aged 40 years and over in 2023. Show all working (2 marks)

vii. How reliable do you think your prediction in the previous question will be? Justify your answer (3 marks)