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**1. An overall view of an employee’s age at SuperPart**

I am interested in the age demographics of our employees. There are various reasons for this. One is to predict the potential retirement rate, as this impacts on our superannuation funding and skill base, as people retire and leave the company.

Another is to establish if SuperPart is attracting enough younger workers, while another is to see if the spread of ages allows for people progressing through the stages of middle management. Accordingly, a general summary of age, of all our employees, is required, for presentation at the next Executive meeting.

**2. Exploring Associations**

I am also interested in how age relates to some specific factors for our employees. In particular, does there appear to be

any relationship between an employee’s age and:

(a) Occupation within SuperPart

(b) The number of hours worked

(c) Before?taxes Income

On the basis of the above, provide a brief summary how the factors compare.

**3. Differences in levels of job satisfaction**

Since the introduction of the national government’s new Industrial Relations laws, the Executive is particularly concerned about the level of contentment and discontentment of our employees.

(a) Can you please provide a summary report on worker satisfaction at SuperPart?

(b) Is there any difference in the level of job satisfaction and union or non?union membership? (I am interested in those employees who say they are satisfied in some way or other with their jobs.)

(c) Are there are any differences in hours worked based on job satisfaction? Can you provide me with a brief summary of which employee groups are working the longest hours.

**4. Worker Retention**

As well as retirement, management is also worried about employees leaving for other reasons. A recent industry?wide survey suggested that 10% of employees anticipate leaving the industry in the next 2 years. If this figure is true at SuperPart, some managers have predicted that the company would lose 1000 or more employees. Are you able to work out the chances of this occurring?

**5. Union Memberships**

You may not be aware, but union membership at SuperPart has never been high. Nonetheless, in the last enterprise bargaining agreement we agreed with the unions that a range of issues such as work hours and job satisfaction would be investigated for all employees. To assist in this goal, and to analyse the extent and role of unionisation in the company, I would like information on the features mentioned below.

(a) What is the estimated average working week for all SuperPart employees? What is the estimated average working week for union members? For non?union members?

(b) Can you provide me with an accurate estimate of the total number of non?union members across the whole organization who would work more than 40 hours? Likewise, how many are working more than 50 hours?

(c) There is some speculation that the non?unionised workers work on average more than 45 hours per week. Is there any way of confirming this?

(d) A recent survey of manufacturers showed that the proportion of unionised staff nationally was at least 20%. I suspect that SuperPart would be on the ‘low?unionised’ side, compared to the country overall. Am I correct in saying that the union is wrong and their membership is below 20%? .

## Answer:

### Introduction:

I am presenting the results obtained from the analysis of the employees’ survey data of SuperPart. There are a total of 9800 employees working in Superpart. It would have become extremely problematic to analyze and study the responses of all the employees. Thus, for simplicity of the analysis, a sample of 400 employees has been selected and their responses have been recorded and analyzed. I assume that the results of this analysis will be sufficient to answer your queries.

### Age profile of the employees at SuperPart

I am presenting the results obtained from the analysis of the employees’ survey data of SuperPart. There are a total of 9800 employees working in Superpart. It would have become extremely problematic to analyze and study the responses of all the employees. Thus, for simplicity of the analysis, a sample of 400 employees has been selected and their responses have been recorded and analyzed. I assume that the results of this analysis will be sufficient to answer your queries.

### Age profile of the employees at SuperPart

It has been observed that the employees of SuperPart has an average age of 39.41 years. The variation of their ages is found to be 10.61 years. The youngest employee of the company was found to be 18 years and the oldest employee of the company is 69 years old. It can also be seen that the age of 50 percent of the employees are more than 38 years. The ages of 25 percent of the employees are less than 32 years and 25 percent of the employees are higher than 46 years. One of the employee has been found to be much high as compared to the other employees.

### Exploring Associations

It has been observed that the mean age of the employees of SuperPart has similarity. The average age is least in the department of Tech or Sales (38.05). The lowest variation in the ages has been observed in the professional department. The average age of the employees in that department is found to be 40.08 years. The highest variability of age has been observed in the department Admin.

### The number of Hours Worked

It has been observed from the analysis that most of the workers of SuperPart usually work for 38 to 47 hours a week. The data shows that there are two employees in the company who work for 88 hours to 97 hours in a week. It has also been found that most of the employees fall under the age group of 28-37 years. Of the employees in that age group, 73 work for 38 to 47 hours a week. The working hours of the employees in the age group of 68 to 77 years is 28 to 37 hours per week and the youngest age group, that is 18 to 27 years old people work between 28 to 77 hours in a week.

It has further been observed that there is very weak relation between age of the employees and their working hours. It is also clear from the analysis that with the increase in age by a year, the working hours decreases by 0.0131 hours.

### Before-Taxes Income

It has been observed that the pre-tax income of most of the employees lie between 30.1 and 40.1 thousand dollars. The pre-tax income of the employees belonging to the age group of 18 to 27 years varies between 30.1 and 80.1 thousand dollars. The highest pre-tax income is received by the employees in the age group of 58 to 67 years. Their income ranges between 110.1 to 120.1 thousand dollars.

It has been observed that there is very weak relation between the pre-tax income of the employees and age of the employees. There is $303.3 increase in the pre-tax income of the employees with the increase in their age by one year.

### Differences in the levels of job-satisfaction

The data shows that 185 employees are satisfied with the work environment of SuperPart, 171 employees are satisfied moderately and only 17 employees are very dissatisfied with the work environment at SuperPart.

### Union Membership and Job Satisfaction

Among the non-union employees, 39 percent are very satisfied and 1 percent is very dissatisfied, whereas, among the union employees, 7 percent of them are very satisfied and 3 percent of them are very dissatisfied.

Considering the analysis in another way, it can be represented that among the employees who are very satisfied, 85 percent are non-union members and only 15 percent belong to some unions. Again, amongst the moderately satisfied employees, 84 percent are non-union members and only 16 percent are union members. Again, 71 percent of the very dissatisfied employees are non-union members and 29 percent are union members.

Further, 47 percent of the non-union employees are very satisfied and 43 percent are moderately satisfied. Thus, only 4 percent of the non-union employees are very dissatisfied with the work environment at SuperPart.

Again, 41 percent of the non-union employees are very satisfied and moderately satisfied. Thus, only 7 percent of the non-union employees are very dissatisfied with the work environment at SuperPart.

### Working Hours and Job Satisfaction

The job satisfaction of employees on the basis of their working hours has been analyzed. It has been observed that a very satisfied employee works on an average of 46.14 hours in a week. Least amount of average working hours (48.08 hours per week) has been observed for the very dissatisfied employees. The moderately satisfied workers show the least variable working hours (7.72 hours per week) whereas the little dissatisfied employees show the highest variation in their working hours (12.47 hours per week).

The very satisfied employees work for a minimum of 28 hours per week and the very dissatisfied employees work for a minimum of 32 hours a week. It has also been observed that 25 percent of the company’s employees work for less than 40 hours per week irrespective of the satisfaction criterions. 50 percent of the satisfied and moderately satisfied employees work within 10 hours per week.

### Worker Retention

To make an estimate for the probable number of employees who will be leaving SuperPart in the coming two years has been determined with the help of a binomial probability model. The results of the analysis stated that 980 employees of the organization are probable to leave the organization in the next two years.

### Union Memberships

**Part a**

Considering all the employees of Superpart it has been seen from the analysis that the mean working hours is 45.45 and the mean working hours of the population has a 95 percent chance to stay within the interval 44.45 and 46.42 hours per week.

Considering the employees having some union membership of Superpart it has been seen from the analysis that the mean working hours of them is 45.14 and the mean working hours of the population has a 95 percent chance to stay within the interval 42.34 and 47.95 hours per week.

Considering the non-union member employees of Superpart it has been seen from the analysis that the mean working hours is 45.49 hours per week and the mean working hours of the population has a 95 percent chance to stay within the interval 44.44 and 46.54 hours per week.

### Part b

In the sample selected, there are 331 non-union members. Among them, 296 work for more than 40 hours in a week which is 89 percent of the non-union members. Thus, it can be said that there is 95 percent chance that 86 to 93 percent of the employees of the organization work for more than 40 hours in a week.

To be more specific, it has further been seen that 102 non-union employees work for more than 50 hours in a week. Thus, it can be said that there is 95 percent chance that 26 to 36 percent of the employees of the organization work for more than 50 hours in a week.

### Part c

The employees who are not union members have an average working hour of 45.49 hours a week. From the analysis it is clear that at 5 percent level of significance, the average working hours of the non-union members is less than 45 hours a week.

### Part d

It has been observed from the analysis that 69 employees of the organization were entitled for some unions. The number of employees who are a member of some unions is less than 20 percent according to the analysis conducted at 1percent, 2 percent and 5 percent levels of significance.

### Future Surveys

To confirm if a sample size of 400 is enough I present the following calculation.

The standard deviation of the working hours of the employees is 10.0455 hours. At 95% confidence level z-value = 1.96. To estimate within 1 hour the number of employees required:

Hence, . or n = 387.66 ≈ 388

Thus, the minimum number of employees required = 388.

Hence, at 95% confidence level 400 employees is enough for estimating the working hours within 1 hour.

At 90% confidence level z-value = 1.6445. To estimate within 1 hour the number of employees required:

Hence, . or n = 273.0 ≈ 273

Thus, the minimum number of employees required = 273.

Hence, at 90% confidence level 400 employees is enough for estimating the working hours within 1 hour.

At 99% confidence level z-value = 2.5758. To estimate within 1 hour the number of employees required:

Hence, . or n = 669.5 ≈ 670

Thus, the minimum number of employees required = 670.

Hence, at 99% confidence level 400 employees is not enough for estimating the working hours within 1 hour.

### Number of Satisfied employees

From the data of 400 employees, it is seen that 356 employees are very or moderately satisfied. Hence, the proportion of satisfied employees is 0.89.

At 95% confidence level z-value = 1.96. To estimate within 1% the number of employees required:

Hence, n = 3760.9 ≈ 3761

Thus, the minimum number of employees required = 3761.

Hence, at 95% confidence level 400 employees is not enough for estimating the number of satisfied employees to within 1%.

At 90% confidence level z-value = 1.6445. To estimate within 1% the number of employees required:

Hence, n = 2648.7 ≈ 2649

Thus, the minimum number of employees required = 2649.

Hence, at 90% confidence level 400 employees is not enough for estimating the number of satisfied employees to within 1%.

In the report discussed above, analysis of the data on the employees of SuperPart has been done. Hopefully, the information provided above will be enough to satisfy the requirement of the vice president of Human Resources.

Thanking You,

Sandy Stedwell

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