# BUS308: Statistics for Managers (Problem Set)

Week 1. |
Measurement and Description – chapters 1 and 2 | |||||||||||||

The goal this week is to gain an understanding of our data set – what kind of data we are looking at, some descriptive measurse, and a | ||||||||||||||

look at how the data is distributed (shape). | ||||||||||||||

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. | ||||||||||||||

Nominal | Ordinal | Interval | Ratio | |||||||||||

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. | ||||||||||||||

Note: Place data to the right, if you use Descriptive statistics, place that to the right as well. | ||||||||||||||

Some of the values are completed for you – please finish the table. | ||||||||||||||

Salary | Compa | Age | Perf. Rat. | Service | ||||||||||

Overall | Mean | 35.7 | 85.9 | 9.0 | ||||||||||

Standard Deviation | 8.2513 | 11.4147 | 5.7177 | Note – data is a sample from the larger company population | ||||||||||

Range | 30 | 45 | 21 | |||||||||||

Female | Mean | 32.5 | 84.2 | 7.9 | ||||||||||

Standard Deviation | 6.9 | 13.6 | 4.9 | |||||||||||

Range | 26.0 | 45.0 | 18.0 | |||||||||||

Male | Mean | 38.9 | 87.6 | 10.0 | ||||||||||

Standard Deviation | 8.4 | 8.7 | 6.4 | |||||||||||

Range | 28.0 | 30.0 | 21.0 | |||||||||||

3 | What is the probability for a: | Probability | ||||||||||||

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

b. Randomly selected male being in grade E? | ||||||||||||||

Note part b is the same as given a male, what is probabilty of being in grade E? | ||||||||||||||

c. Why are the results different? | ||||||||||||||

4 | A key issue in comparing data sets is to see if they are distributed/shaped the same. We can do this by looking at some measures of where | |||||||||||||

some selected values are within each data set – that is how many values are above and below a comparable value. | ||||||||||||||

For each group (overall, females, and males) find: | Overall | Female | Male | |||||||||||

A | The value that cuts off the top 1/3 salary value in each group | “=large” function | ||||||||||||

i | The z score for this value within each group? | Excel’s standize function | ||||||||||||

ii | The normal curve probability of exceeding this score: | 1-normsdist function | ||||||||||||

iii | What is the empirical probability of being at or exceeding this salary value? | |||||||||||||

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

i | The z score for this value within each group? | |||||||||||||

ii | The normal curve probability of exceeding this score: | |||||||||||||

iii | What is the empirical probability of being at or exceeding this compa value? | |||||||||||||

C | 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? | ||||||||||||||

Conclusions from looking at salary results: | ||||||||||||||

Conclusions from looking at compa results: | ||||||||||||||

Do both salary measures show the same results? | ||||||||||||||

Can we make any conclusions about equal pay for equal work yet? | ||||||||||||||