Minitab assignment4

Chapter 13 Minitab Express

The activity includes three questions. Using the data in the textbook dataset, answer the

following questions:

Question 1:

Using the data in the textbook dataset, explore the relationship of the public safety expenditures

to county median family income level. Create a scatterplot and describe what you see.

I will use different variables to demonstrate how you would work with this type of question. We’ll

explore whether Human Services expenditures (C33) vary by county mean household income

(C40).

Let’s look at a scatterplot to get an idea of the relationship between these two variables.

Use Graph, Scatterplot, Simple and we’ll select these two variables:

Here is the scatterplot. We see that as the income increases, expenditures increase.

Question 2:

Create a new variable that categorizes median household income level into 3 groups (low,

medium, high. Create at least one graphical display showing public safety expenditures by the 3

categories of median family income. Describe how public safety expenditure varies by the

median family income categories.

I will use mean household income (C40) and create a variable titled Income Level with Low

(lowest 33 counties), Medium (middle 34 counties) and High (top 33 counties).

It is easiest to use the rankings to create these new variables so I’ll rank the column and then

use the ranks to create the new variables.

Using Data, Rank, for Mean Household Income; Minitab Express will place the ranks in the next

blank column, C79.

To create the new variable, we use Data, to text. See below. This will be stored in C80.

Here is a screen shot of the first few rows. I added the title to C80.

I will investigate the effect of income levels on Human Services expenditures (C33) using

boxplots. You can also use histograms, dotplots, etc. Select Graphs, Boxplot, with groups,

select the variable you want to graph, and the categorical variable for grouping (C80 in this

example).

Here are the boxplots:

I see that as income rises, the human service expenditures also rise. This agrees with the

scatterplot from question 1. I see some outliers in the low and high groups that I might want to

investigate.

Question 3:

Test the hypothesis that the public safety expenditures vary by county median family income

level.

 State the research and null hypotheses.  To test the hypothesis, would you use a chi-square test or t-test? Justify your choice.  Perform the appropriate statistical procedure. Based on the analysis, would you reject

your null hypothesis? What evidence did you use to make your decision?

State the research and null hypotheses:

I will will explore whether Human Services expenditures (C33) vary by county mean household

income (C40).

My research hypothesis and null hypotheses are:

H1: As mean income increases, HS expenditures increase.

H0: The level of HS expenditures does not differ with mean income.

To test the hypothesis, would you use a chi-square test or t-test? Justify your choice.

I will use a chi-square test (why??).

Perform the appropriate statistical procedure. Based on the analysis, would you reject

your null hypothesis? What evidence did you use to make your decision?

I have created the income categories in question 2. I need to create the human services

expenditure categories. I will create a variable titled HS Categories with Low (lowest 33

counties), Medium (middle 34 counties) and High (top 33 counties). See the instruction in

question 2 for guidance. I calculated the HS ranks and put these in C81 and then the

categories were calculated and placed in C82. Here is a screen shot of the first few rows:

Now I can use these new variables in a chi-square analysis. We use Statistics, Cross

Tabulation and Chi-square test. Select the row and column variables. Click Display to select

the Chi-square test and show the expected cell counts and each cell’s contribution to chi-

square, then click OK.

Here is the output:

We see that the Pearson Chi-Square has a p-value of 0.0002 which tells us that the level of

expenditure is not independent of the income level; we can say that HS expenditure is

associated with the income level.

Examining the cell contribution to the chi-square, the cell with high HS expenditure and high

income is contributing the most. This agrees with the boxplots from question 2. We could also

explore this further by examining other characteristics of the counties that fall into this cell.