Lab Project

LAB Unit 4: Stat Project [(Required/Graded) 25 points) CSLO D, CSLO G]

The goal of this lab is to understand and find simple probabilities and conditional probabilities, and to use the Multiplication Rule and the Addition Rule.

1. List the name for your qualitative variable, V1

 

2. Return to Lab 2. List the name for one of the largest slice in your pie chart. (If a tie, choose either one.)

This name will be the label for Column 1 in your chart.

 

3. Categorize all of the other slices of your graph with a logical label. (This will be very easy if your graph has only two slices; you use the name of the smaller slice. If there are more than two slices, use the labels ‘others’ or a better group name.)

This name will be the label for Column 2 in your chart.

 

4. List the name for your quantitative variable, V2.

 

5. Return to Lab 3, Part 1. What is the median for your V2 ?

 

6. The label for Row 1 will be values at or below the median. For example, if the median $ value of the investment 50 thousands, Row 1 will be labeled ‘investment under ’ or ‘investment equal to 50 thousands or less’ ()

What is your label for Row 1?

 

7. The label for Row 2 will be values above the median. For example, if the median investment is 50 thousands, Row 2 will be labeled ‘over 50 thousands’. (> 50)

What is your label for Row 2?

 

Use the information above to create a table similar to this one.

Qualitative Variable, Political Party

Below are examples (with a sample of n=40)

 

Drug

Others

Total

()(000)

6

8

14

>50(000)

19

7

26

Total

25

15

40

Quantitative

Variable, V2

Age

8. Return to data in Lab 1 and count up the observations for each of the four cells in the table. Place the sums in each cell and be sure that your frequencies add to 100. Also record the totals for each row and each column.

Qualitative Variable, ______________

Quantitative

     

Total

       
       
       

Variable, V2

Find simple probabilities.

9. Compute the probability of being in Row 1. Use the language of your data. (For example, P () = ).

10. Compute the probability of being in Row 2. Use the language of your data. (For example, P(>50) = ).

11. Compute the probability of being in Column 1. Use the language of your data. (For example, P(Drug) = ).

12. Compute the probability of being in Row 1 and Column 1 using the appropriate frequency from your table. Use the language of your data. (For example, P(Drug and) = ).

Find conditional probabilities.

13. Find the probability of being in Row 1, given Column 1. Use the language of your data.

14. (a) Comparing the probability in # 13 to the probability in # 9, decide if Rows and Columns are independent. (b) Clearly explain your reasoning, using a complete sentence and one of these phrases: equally likely, more likely or less likely.

Example

Your Data

13. P(, given Drug) =

14. P() = 0.350

Since P(, given Drug) is less than P(), Drug are less likely to be . These are dependent events.

13.

14.

15. Find the probability of being in Column 1, given Row 2. Use the language of your data. (For example, P(Drug, given >50).

16. comparing the probability in #15 to the probability in #11, determine if Rows and Columns are independent. Clearly explain your reasoning, using a complete sentence and one of these phrases: equally likely, more likely or less likely.

Example

Your Data

15. P(Drug, given >50) =

16. P(Drug) = 0.625

Since P(Drug, given > 50) is higher than P(Drug), investment >$50 are more likely to be Drug. These are dependent events.

15.

16.

Multiplication Rule

17. If you choose two subjects from your sample, use the Multiplication Rule to find the probability that they are both from Column 1.

Example

Your Data

P(Both Drugs) =

P(Drug and Drug) = =0.385

17.

Addition Rule

18. Use the Addition Rule to find the probability of being in Row 1 or Column 1.

19. Use the Addition Rule to find the probability of being in Row 1 or Row 2.

Example

Your Data

18. P(investment $ or Drug ) =

19. P(Investment $ or > 50) =

18.

19.

20. Consider your last two answers and list two mutually exclusive events for your data. Explain your reasoning.