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## 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.

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.