Thursday, February 5, 2009

Testing

Sample for Quiz

1. What is Data Modeling?
Data modeling is the act of exploring data-oriented structures. Like other modeling artifacts data models can be used for a variety of purposes, from high-level conceptual models to physical data models. From the point of view of an object-oriented developer data modeling is conceptually similar to class modeling. With data modeling you identify entity types whereas with class modeling you identify classes. Data attributes are assigned to entity types just as you would assign attributes and operations to classes. There are associations between entities, similar to the associations between classes – relationships, inheritance, composition, and aggregation are all applicable concepts in data modeling.
Traditional data modeling is different from class modeling because it focuses solely on data – class models allow you to explore both the behavior and data aspects of your domain, with a data model you can only explore data issues. Because of this focus data modelers have a tendency to be much better at getting the data “right” than object modelers. However, some people will model database methods (stored procedures, stored functions, and triggers) when they are physical data modeling.
How are Data Models Used in Practice?
Although methodology issues are covered later, we need to discuss how data models can be used in practice to better understand them. You are likely to see three basic styles of data model:
· Conceptual data models. These models, sometimes called domain models, are typically used to explore domain concepts with project stakeholders. On Agile teams high-level conceptual models are often created as part of your initial requirements envisioning efforts as they are used to explore the high-level static business structures and concepts. On traditional teams conceptual data models are often created as the precursor to LDMs or as alternatives to LDMs.
· Logical data models (LDMs). LDMs are used to explore the domain concepts, and their relationships, of your problem domain. This could be done for the scope of a single project or for your entire enterprise. LDMs depict the logical entity types, typically referred to simply as entity types, the data attributes describing those entities, and the relationships between the entities. LDMs are rarely used on Agile projects although often are on traditional projects (where they rarely seem to add much value in practice).
· Physical data models (PDMs). PDMs are used to design the internal schema of a database, depicting the data tables, the data columns of those tables, and the relationships between the tables. PDMs often prove to be useful on both Agile and traditional projects and as a result the focus of this article is on physical modeling.





The average weight in kilograms for girls of various ages in the United States is given in the table below

Age in years .5 1 2 3 4 6 8 10
Weight in kg. 7.2 9.1 11.3 13.6 15 20.4 25.4 31.3

REMEMBER TO Clrlist BEFORE YOU BEGIN

1 TO GRAPH A SET OF DATA
press STAT
choose 1:Edit
enter the data in the lists
press ENTER after each piece of data
x-values in one list
y-values in another
be sure that both lists have the same number of
entries
press 2nd Y= (STAT PLOT)
press ENTER
select On
Type: scatterplot
XList: L1
YList: L2
Mark: whichever you like
(the + works best)
press ZOOM 9
You should have a graph

2. TO FIND THE EQUATION FOR THE REGRESSION LINE
press STAT
select CALC
select 4: LinReg (ax+b)
you will want the calculator to graph this along with the data
points you already have graphed
with the cursor as in the picture at the right
press 2nd 1 , 2nd 2 , VARS
select Y-VARS, select 1: Function, select 1: Y1
press ENTER
the equation is given in slope
intercept form where a is
slope and b is the y-intercept
Press Y= to see that the regression equation is
already in the function menu
press GRAPH
your line will be drawn in the
scatterplot

3. TO PREDICT A VALUE NOT GIVEN BY THE DATA
For example: We want to know what a 7 year old girl would be expected to weigh.
press 2nd MODE (QUIT) CLEAR
this will put you back on the regular work screen
input your value on the work screen
press 7 STOX,T,n ENTER
press VARS
select Y-VARS
select 1:Function
press ENTER
select 1:Y1 this is the regression line you defined
press ENTER
press ENTER again to display the value calculated
using your regression line
So a girl 7 years old weighs 23.255 kg



1. In a laboratory experiment on the growth of insects, there were 74
insects three days after the beginning of the experiment and 108 insects
five days after the beginning of the experiment.
a) Find an exponential model for the data algebraically.
b) Find the number of insects at the beginning of the experiment.
c) Predict the number of insects that will be present on the 8th day.

2. The data below was obtained from the U.S. Office of Management and
Budget. The data show that the national debt of the United States has
been increasing significantly since 1965. Use your graphing calculator to
find an exponential model of the form y = abx to represent the data in the
table.
Year Amount of debt (in billions)
1965 322
1970 381
1975 542
1980 909
1985 1818
1990 3207
1995 4921

a) Write the equation for your model.
b) Use your model to estimate the debt in 1982. Since this value falls within the data we have this process is called interpolation.
c) Use your model to estimate the debt in 2005. Since this value is beyond known values of the data, this process is called extrapolation.

Day 0 1 2 3 4 5
Price 350 340 320 290 250 200

The data in the table below shows the average weight gain of three pigs on a hog farm. Twenty-four pigs were each given a dietary supplement in the form of pellets. The pigs were randomly selected to receive a daily dosage of pellets ranging from 0 to 7 pellets, the average weight gain of the three pigs receiving the same dosage is summarized in the table below.
No of pellets Percentage of (daily dosage) weight gain
0 10
1 13
2 21
3 24
4 22
5 20
6 16
7 13

i) Draw a scatterplot of the data in the table
ii) What model fit the data well. Explain your answer.
iii) Find an appropriate model for the data.
iv) Determine the best dosage to give to the hogs based on the data.



Based on tests made by the Bureau of Public Roads, below are the distances (in feet) it takes to stop a car in minimum time under emergency conditions.
Reaction time is considered to be .75 seconds.
Speed (mph) 10 20 30 40 50 60 70
Stopping Distance (feet) 19 42 73 116 173 248 343

Make a scatterplot of the data.
Find an appropriate equation to model this data. Write the equation.
Using your model fill in the expected stopping distances for each speed listed in the table below.

Speed (mph) 15 25 35 55 75 90 100
Stopping Distance (feet)