Question:
As for Assignment 1, you are playing the role of John Frank, junior Analyst at Cuteen. Lee Maston, Human Resources Manager at Cuteen has written to you again regarding the Cuteen dataset. His memorandum is reproduced here:
For Attention: John Frank, Senior Analyst
From: Lee Maston, Human Resources Manager
Regarding: Further analysis of dataset
Dear John, Thank you for your earlier responses. In order for me to finalise the employee profile required by senior management, I need the following information.
1. An estimate of: a. The mean hours worked for ALL Cuteen employees.
b. The proportion of ALL Cuteen employees who are very likely to stay in their job.
2. The mean number of hours worked across the industry is 48 per week. Senior management claims that our employees work fewer hours than the industry average. Can you please check the validity of this claim?
3. Senior management also believes that the proportion of employees likely to stay in the job is more than 40%. Can you please check and verify whether this claim is true.
4. Is there a significant difference in the mean number of hours worked of ALL male and ALL female employees?
Activity
Part 2: Response to Lee
1. (a ) An estima te of the mean hours worked by all Cuteen employees.
1. (b ) The proportion of employees who are very likely to stay in their job
2. The mean number of hours worked across the industry is 48 per week. Senior management claims that our employees work fewer hours than the industry average. Can you please check the validity of this claim?
3. Senior management also believes that the proportion of employees very likely to stay in the job is more than 40%. Is this true?
4. Is there is a significant difference in the mean number of hours worked by ALL male and ALL female employees?
5. Lee is concerned that a sample of 450 employees may not provide very accurate estimates. What sample size is required to ensure: a. the mean number of hours worked for ALL Cuteen employees is accurate to within 2 hours, with 95% confidence?
b. the proportion of ALL Cuteen employees who are very likely to stay with their job to within 5%, with 95% confidence?
6. Lee would like to know whether Gross salary last year was affected by the Years of full-time employment (provide solutions for a, b, c, d).
Answer
1.The estimate mean of working hours spent by all Cuteen employees holds the value 45.26888889 » It suggests that the entire data is centred at the single value 45. It shows that most of the employees are working in the company with an average of 45 working hours. However, if there is presence of outliers or any extreme value then the interpretation of mean is violated.
The estimate of the proportion of all Cuteen employees who are very likely to stay in their job is obtained by using a Pivot table and chart. The number of employees whose Stayorg variable’s value is “very likely” is first calculated and the count is divided by 450 which is the total number of Cuteen employees. Then, the pie chart and bar chart are plotted which show the percentage of very likely as 17.78%. Thus the estimate of the proportion can be written as 0.1778.
2.According to the calculation of problem 1(a), the average value of working of the Cuteen employees is 45. Thus it is less than the industry average working hours and the claim of the senior management is valid and true. Comparison between the mean values can be taken as the proof of the validity of the claim.
3.The senior management’ belief on the proportion of the employees who like to stay in the job is to be checked from the calculation performed on the Excel sheet. From the graph (bar chart and pie chart), it is clearly seen that the percentage of proportion of likely to stay employees is 42.22% which is 2.2% more than 40%. Thus, the senior management’s claim is true in this case and the claim is mathematically valid.4.The significant difference of the mean number of working hours between male and female employees can be represented by pivot table with the sum of working hours based on males and females. First, the calculation of descriptive statistics is calculated separately for all males and females. Then, the pivot table is evaluated which shows that sum of hours worked for males is 61.02% and that for female sis 38.90%. Thus, it can be concluded that there is significant difference between these two sums of hours worked.
5.The sample size helps to determine how many observations one needs to be estimated for any parameter. The size of the sample size depends mainly on three factors-
i. Magnitude of the margin of error as larger the sample size, smaller is the margin of error.
- Confidence level; larger confidence level requires larger sample size.
iii. The variability; if the standard deviation is large, then sample size is required to be large.
The sample size is calculated using the formula n = σ2z2/m2; where z = confidence coefficient, σ = standard deviation, m = margin of error.
- Thus, for the mean number of working hours for all Cuteen employees, the sample size should be, n =27274932 * (1.96)2 /22 ≈ 92.
- The sample size, required to calculate the proportion who are very likely to stay with the job, is n ≈ 49.
6.The scatter plot shows quite good correlation between working hours and salary. Also, there is positive correlation between the working hours and wok years. The regression equation is given as Y = 42.25530642 + 0.138186 X
1 + 0.035420 X
2 + 0.041514 X
3. It shows that for one unit change in X
1, X
2, and X
3, Y changes by 0.138 units, 0.0354 units, and 0.0415 units respectively.
