week4 live lecture statistics for decision making

B Heard

Week 4 LectureStatistics For Decision

Making(Week 4 Lab)

Not to be used, posted, etc. without my expressed permission. B Heard

This week we will be looking at examples that are similar to your Lab for this week. We will look at:Working with a Contingency Table (or Cross-

Reference Table) and determining probabilities based on the table

A Binomial Probability Distribution example, and

A Poisson Probability Distribution example

Week 3 Quiz


Week 3 Quiz

Working with Contingency Tables


Let’s say that we have a milk truck that is delivering three types of milk (Whole, Skim, and Chocolate) to two parts of town (East and West)

Contingency Table Example


We developed a Contingency Table based on the type of milk and the area of town it is being delivered. It is on the page that follows.



Side of Town

Milk Type East West Totals

Whole Milk 27 28 55

Skim Milk 21 19 40

Chocolate Milk 9 12 21

Totals 57 59 116



Side of Town


Whole Milk 27 28 55

Skim Milk 21 19 40


Totals 57 59 116

What does this table tell us?• It gives us the specific types of milk delivered to each side of

town. Note that the Vertical Totals and the Horizontal Totals are the same (they have to be)

Let’s look at some questions… Find:1. P(Skim milk)2. P(West side)3. P(Chocolate AND going to the East side)4. P(Whole OR going to the East side)5. P(Skim milk|West Side) (read probability of it

being skim milk given that it’s going to the West side)

6. P(West side|Skim milk) (read probability of it going to the West side given that it’s Skim milk)

7. Are “Chocolate” and “Going to the East side” independent or dependent?




Side of Town


Whole Milk 27 28 55

Skim Milk 21 19 40


Totals 57 59 116

1. P(Skim milk)

40/116 or 0.3448 or 34.48%



Side of Town


Whole Milk 27 28 55

Skim Milk 21 19 40


Totals 57 59 116

2. P(West side)

59/116 or 0.5086 or 50.86%



Side of Town


Whole Milk 27 28 55

Skim Milk 21 19 40


Totals 57 59 116

3. P(Chocolate AND going to the East side)

9/116 or 0.0776 or 7.76%



Side of Town


Whole Milk 27 28 55

Skim Milk 21 19 40


Totals 57 59 116

4. P(Whole OR going to the East side)(55+57-27)/116 (you must subtract overlap so that you

don’t count twice)



Side of Town


Whole Milk 27 28 55

Skim Milk 21 19 40


Totals 57 59 116

4. P(Whole OR going to the East side)(55+57-27)/116, thus our answer is85/116 or 0.7328 or 73.28%



Side of Town


Whole Milk 27 28 55

Skim Milk 21 19 40


Totals 57 59 116

5. P(Skim milk|West side), the probability that is skim milk given that it’s going to the West side.

19/59 or 0.3220 or 32.20%

It is given that it’s going to the West side, so we are only dealing with those 59…



Side of Town


Whole Milk 27 28 55

Skim Milk 21 19 40


Totals 57 59 116

6. P(West side|Skim milk), the probability that it’s going to the West side given that it’s Skim Milk.

19/40 or 0.475 or 47.5%It is given that it’s Skim milk, so we are only dealing with those 40…


Contingency Table Example7. Are “Chocolate” and “Going to the East side”

independent or dependent?

Break this down and draw lines if you need to…..

“Chocolate” and “Going to the East side” independent or dependent?

Is P(Chocolate) = P(Chocolate|East Side)

In other words is the probability of it being Chocolate milk equal to the probability of being Chocolate milk GIVEN THAT it’s going to the East side.If they are equal they are Independent, if they are not – they are Dependent.



Side of Town


Whole Milk 27 28 55

Skim Milk 21 19 40


Totals 57 59 116

P(Chocolate) = 21/116



Side of Town


Whole Milk 27 28 55

Skim Milk 21 19 40


Totals 57 59 116

P(Chocolate|East Side) = 9/57


Contingency Table ExampleP(Chocolate) is not equal to P(Chocolate|East

Side)21/116 is not equal to 9/57

Thus they are

Dependent!

Don’t forget you can easily use Excel for your Contingency Table Calculations

Contingency Table

Side of Town Milk Type East West TotalsWhole Milk 27 28 55Skim Milk 21 19 40Chocolate Milk 9 12 21Totals 57 59 116

Fraction Decimal PercentageP(skim milk) 40/116 0.344827586 34.48%P(West Side) 59/116 0.50862069 50.86%P(Choc AND going to the East) 9/116 0.077586207 7.76%P(Whole OR going to the East) 85/116 0.732758621 73.28%P(skim milk|west side) 19/59 0.322033898 32.20%P(West Side|skim milk) 19/40 0.475 47.50%

Week 3 Quiz

Binomial Distribution



Binomial Distribution• The tutorials are very clear on how to do

these, however I am going to show you a template that I use at work. I feel part of my job as an instructor and as a lecturer is to share my professional experience with you.

• A surgical technique is performed on seven patients. You are told there is a 70% chance of success. Find the probability that the sugery is successful for:

a. exactly five patients. b. at least five patients. c. less than five patients.

Sox = number of patients for whom the surgery was successful; p = probability of success = 0.70; n = number of patients having surgery = 7

• Go to the following website:

• http://highered.mcgraw-hill.com/sites/0070620164/student_view0/excel_templates.html

• Click on Excel File that says Binomial, and save to your computer

• Open the file• First thing, click on the “Review” Tab at the

top and click on “Unprotect Sheet”. You have to do this to be able to use it.

• Now just input your “n” and your “p”…. (next page)


Binomial Distribution

http://highered.mcgraw-hill.com/sites/0070620164/student_view0/excel_templates.html



Binomial Distribution• A surgical technique is performed on seven patients. You are told

there is a 70% chance of success. Find the probability that the sugery is successful for:

a. exactly five patients. b. at least five patients. c. less than five patients.

x = number of patients for whom the surgery was successful; p = probability of success = 0.70; n = number of patients having surgery = 7


Binomial Distribution• Let’s find our answers for the questions

a. exactly five patients. Answer is 0.3117 or 31.17% b. at least five patients. Answer is 0.6471 or 64.71% c. less than five patients. This would be “At Most 4” Answer 0.3529 or 35.29%

c

a

b

Week 3 Quiz

Poisson Distribution



Poisson Distribution• The tutorials are very clear on how to do

these, however again I am going to show you a template that I use at work.

• A newspaper finds that the mean number of typographical errors per page is 4. Find the probability that:

a. exactly three typographical errors will be found on a page. b. at most three typographical errors will be found on a page c. more than three typographical errors will be found on a page.

Solution: Define "success" as "a typographical error will be found on a page".

x = number of typographical errors found on a page; μ = mean number of typographical errors found on a page = 4

• Go to the following website again:

• http://highered.mcgraw-hill.com/sites/0070620164/student_view0/excel_templates.html

• Click on Excel File that says Poisson, and save to your computer

• Open the file• First thing, click on the “Review” Tab at the

top and click on “Unprotect Sheet”. You have to do this to be able to use it.

• Now just input your “Mean”…. (next page)


Poisson Distribution




Poisson Distribution• A newspaper finds that the mean number of typographical errors per

page is 4. Find the probability that:

a. exactly three typographical errors will be found on a page. b. at most three typographical errors will be found on a page c. more than three typographical errors will be found on a page

x = number of typographical errors found on a page; μ = mean number of typographical errors found on a page = 4


Poisson Distribution• Let’s find our answers for the questions

a. exactly three typographical errors will be found on a page. Answer 0.1954 or 19.54% b. at most three typographical errors will be found on a page. Answer 0.4335 or 43.35% c. more than three typographical errors will be found on a page (this would be “at least 4”) so Answer 0.5665 or 56.65%

b

a

b


Poisson Distribution• Please note that you also have the graphs

when using these templates.

I will post charts and linkson my Facebook page at

www.facebook.com/statcave

SSTAT CAVE


week4 live lecture statistics for decision making

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