**BUS 308 Statistics for Managers, New Syllabus**

**Assignment, Measurement and Description Chapters 1 and 2**

1. Measurement issues. Data, even numerically coded variables, can be one of 4 levels -nominal, ordinal, interval, or ratio. It is important to identify which level a variable is, as this impact the kind of analysis we can do with the data. For example, descriptive statistics such as means can only be done on interval or ratio level data. Please list under each label, the variables in our data set that belong in each group.

b. For each variable that you did not call ratio, why did you make that decision?

2. The first step in analyzing data sets is to find some summary descriptive statistics for key variables. For salary, compa, age, performance rating, and service; find the mean, standard deviation, and range for 3 groups: overall sample, Females, and Males. You can use either the Data Analysis Descriptive Statistics tool or the Fx =average and =stdev functions. (the range must be found using the difference between the =max and =min functions with Fx) functions.

3. What is the probability for a:

a. Randomly selected person being a male in grade E?

b. Randomly selected male being in grade E?

c. Why are the results different?

4. For each group (overall, females, and males) find:

a. The value that cuts off the top 1/3 salary in each group.

b. The z score for each value:

c. The normal curve probability of exceeding this score:

d. What is the empirical probability of being at or exceeding this salary value?

e. The value that cuts off the top 1/3 compa in each group.

f. The z score for each value:

g. The normal curve probability of exceeding this score:

h. What is the empirical probability of being at or exceeding this compa value?

i. How do you interpret the relationship between the data sets? What do they mean about our equal pay for equal work question?

5. What conclusions can you make about the issue of male and female pay equality? Are all of the results consistent? What is the difference between the sal and compa measures of pay?

**Discussion 1**: Language

**Discussion 2**: Levels

**BUS 308 Week 1 Quiz (03 Sets)**

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**Assignment, Testing Means – T-test**

In questions 2 and 3, be sure to include the null and alternate hypotheses you will be testing. In the first 3 questions use alpha = 0.05 in making your decisions on rejecting or not rejecting the null hypothesis.

1. Below are 2 one-sample t-tests comparing male and female average salaries to the overall sample mean. (Note: a one-sample t-test in Excel can be performed by selecting the 2-sample unequal variance t-test and making the second variable = Ho value -- see column S). Based on our sample, how do you interpret the results and what do these results suggest about the population means for male and female average salaries?

2. Based on our sample data set, perform a 2-sample t-test to see if the population male and female average salaries could be equal to each other. (Since we have not yet covered testing for variance equality, assume the data sets have statistically equal variances.)

b. Since the one and two sample t-test results provided different outcomes, which is the proper/correct approach to comparing salary equality? Why?

3. Based on our sample data set, can the male and female compas in the population be equal to each other? (Another 2-sample t-test.)

4. Since performance is often a factor in pay levels, is the average Performance Rating the same for both genders?

5. If the salary and compa mean tests in questions 2 and 3 provide different results about male and female salary equality, which would be more appropriate to use in answering the question about salary equity? Why?

What are your conclusions about equal pay at this point?

**Discussion 1**: t-Test

**Discussion 2: ** Variation

**BUS 308 Week 2 Quiz (03 Sets)**

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**Assignment, AVONA and paired T-test**

At this point we know the following about male and female salaries.

a. Male and female overall average salaries are not equal in the population.

b. Male and female overall average compas are equal in the population, but males are a bit more spread out.

c. The male and female salary range is almost the same, as is their age and service.

d. Average performance ratings per gender are equal.

Let's look at some other factors that might influence pay - education (degree) and performance ratings.

a. Last week, we found that average performance ratings do not differ between males and females in the population. Now we need to see if they differ among the grades. Is the average performance rating the same for all grades? (Assume variances are equal across the grades for this ANOVA.)

2. While it appears that average salaries per each grade differ, we need to test this assumption. Is the average salary the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.). Use the input table to the right to list salaries under each grade level.

3. The table and analysis below demonstrate a 2-way ANOVA with replication. Please interpret the results.

4. Many companies consider the grade midpoint to be the "market rate" - what is needed to hire a new employee. Does the company, on average, pay its existing employees at or above the market rate?

5. Using the results up thru this week, what are your conclusions about gender equal pay for equal work at this point?

**Discussion 1**, ANOVA Testing

**Discussion 2,** Effect Size

**BUS 308 Week 3 Quiz (02 Sets)**

**Assignment, Confidence Intervals and Chi Squares (Chs 11 – 12)**

For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions.

For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed.

1. Using our sample data, construct a 95% confidence interval for the population's mean salary for each gender. Interpret the results. How do they compare with the findings in the week 2 one sample t-test outcomes (Question 1)?

2. Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population. How does this compare to the findings in week 2, question 2?

Why is using a two sample tool (t-test, confidence interval) a better choice than using 2 one-sample techniques when comparing two samples?

3. We found last week that the degree values within the population do not impact compa rates. This does not mean that degrees are distributed evenly across the grades and genders. Do males and females have the same distribution of degrees by grade?

4. Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population? What are the hypothesis statements:

5. How do you interpret these results in light of our question about equal pay for equal work?

**Discussion 1:** Confidence Intervals

**Discussion 2:** Chi-Square Tests

**BUS 308 Week 4 Quiz (03 Sets)**

**BUS 308 Week 5 Correlation and Regression**

For each question involving a statistical test below, list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. For full credit, you need to also show the statistical outcomes - either the Excel test result or the calculations you performed.

1. Create a correlation table for the variables in our data set. (Use analysis ToolPak function Correlation.)

Interpret the results. What variables seem to be important in seeing if we pay males and females equally for equal work?

2. Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Mid, age, ees, sr, raise, and deg variables.) (Note: since salary and compa are different ways of expressing an employee’s salary, we do not want to have both used in the same regression.)

3. Perform a regression analysis using compa as the dependent variable and the same independent variables as used in question 2. Show the result, and interpret your findings by answering the same questions. Note: be sure to include the appropriate hypothesis statements.

4. Based on all of your results to date, is gender a factor in the pay practices of this company? Why or why not? Which is the best variable to use in analyzing pay practices - salary or compa? Why?

Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question? What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test?

**Final Paper: **Identify an issue in your life (work place, home, social organization, etc.) where a statistical analysis could be used to help make a managerial decision. Develop a sampling plan, an appropriate set of hypotheses, and an inferential statistical procedure to test them. You do not need to collect any data on this issue, but you will discuss what a significant statistical test would mean and how you would relate this result to the real-world issue you identified. Your paper should be three to five pages in length (excluding the cover and reference pages). In addition to the text, utilize at least three sources to support your points. No abstract is required. Use the following research plan format to structure the paper:

**Discussion 1**: Correlation

**Discussion 2: **Regression