# statistics help 6

Background

Aegis Inc. is a home inspection firm based in the Northern Virginia area. The President of the company, Ms. Rose Wilson, is concerned about the morale of the sales team. Ms. Wilson had contracted a local firm to survey the employees of Aegis Inc. and the results were delivered to her in an EXCEL spreadsheet. She has tasked her Vice President of Human Resources, Mark Wolfe, to analyse the results of the survey and to report the results to her. Ms. Wilson told Mark that she was concerned about the attitudes of the sales force. In addition to the questions that were asked some additional data were recorded: the most recent base annual salary, commission and total pay, the years of seniority, the sales region of the individual, the gender (0=male, 1=female) and the number of contracts written in the pay period.

The survey instructions indicated that the first 5 questions were measured using a 5-point scale using the following key: 1 = strongly disagree, 2 = disagree, 3 = neither agree nor disagree, 4 = agree, 5 = strongly agree. The questions were as follows:

Q1: Aegis Inc. has a good mentoring program

Q2: Aegis Inc. is committed to delivering good value to customers

Q3: Aegis Inc. has very traditional and conservative values

Q4: Aegis Inc. company practices favor men

Q5: Aegis Inc. has a lot of internal power politics.

The final question used a 1-10 scale:

Q6: On a numeric scale, where 0 means totally autocratic and 10 means totally democratic, how would you rate the management style at Aegis Inc.?

There are only 2 divisional managers for Aegis Inc. The geographic regions of the sales team are as follows:

 Region Number Divisional Manager Area Size of Sales Force 1 A South East 60 2 A North East 93 3 A Midwest 59 4 B South West 49 5 B Mountain States 80 6 B West Coast 67 Total 408

Region 4 was only established eight months ago. Prior to that time, the branches were part of Regions 1, 5 and 6.

INSTRUCTIONS

As a group: Answer the following questions involving Descriptive Statistics

Draw (create) a random sample of 50 from the full database then answer the following questions. You will ultimately use the sample of 50 from the full population of 408 to compare and contrast the sample and the population in the questions below. Typically you would not have the data for the entire population (such as in an election). So the point of this project is to use various statistical methods to examine how well your sample matches the population. It is obvious that the charts, figures etc. for the population should be the same for each group (or individual) that does this project. However, I would not expect to see the same results for any two groups (or individuals) samples since they are created using the Random number generator (RNG) mentioned below. This is a detailed and important project in this course, start early and take the time to do a good job. This assignment is worth twice what any one exam is worth.

1. Draw a random sample of 50 from the full population provided by using the Random number generator (RNG) in Excel as a random sampling method (see my example of the RNG under Course documents). After creating the sample of fifty paste it here under this question.

1. Describe how the random sample was taken. Discuss. This is the place that you discuss how you did number 1 above. Be detailed. Refer to the instructions for the RNG that are provided in the Excel document.

1. Determine the mean, mode, median, variance, standard deviation, high value, low value and range for years of seniority, base salary, commission and total salary for your SAMPLE. Save yourself some work here by using the Excel Descriptive statistics function.

1. Determine the mean, mode, median, variance, standard deviation, high value, low value and range for years of seniority, base salary, commission and total salary for the POPULATION. Save yourself some work here by using the Excel Descriptive statistics function.

1. Briefly explain the differences between the population and your sample. Discuss. I am looking for a paragraph or so here of prose. I would expect more than a few sentences.

1. Briefly explain the similarities between the population and your sample. Discuss. I am looking for a paragraph or so here of analysis. I would expect more than a few sentences.

1. Is there a difference between your sample and the population in how the sales force is distributed within the regions? (Is the number of sales people in each of your sample regions proportionally the same as in the total population?) The best way to answer this is to set up a table of the regions in the population and the sample. The table would show how many people are associated with each region. Does the sample mimic the population? Discuss. Again, I am looking for analysis here so I would expect more than a few sentences.

Answer the following questions involving Inferential Statistics

1. Is there a relationship between years of seniority and base pay for the sample? The population? (Hint: Use a Scatter chart- the scatter chart is required and should be displayed for this question.) If you determine if there is a relationship comment if the relationship is linear, curvilinear or something else. Does it change as the values change? Discuss fully.

1. Is there a relationship between years of seniority and commission pay for the sample? The population? (Hint: Use a Scatter chart- the scatter chart is required and should be displayed for this question.) If you determine if there is a relationship comment if the relationship is linear, curvilinear or something else. Does it change as the values change? Discuss fully.

1. Is there a relationship between years of seniority and total pay for the sample? The population? (Hint: Use a Scatter chart- the scatter chart is required and should be displayed for this question.) If you determine if there is a relationship comment if the relationship is linear, curvilinear or something else. Does it change as the values change? Discuss fully.

1. Is there a large or small difference in your answers for the sample and the population for questions 8, 9 and 10? (Hint: Compare the Scatter charts- the scatter charts in the prior questions can be referred to or you can copy them here.) Discuss fully.