EPE / EDP 557 Homework 7

Transcription

1 Section III. A. Questions EPE / EDP 557 Homework 7 Section III. A. and Lab 7 Suppose you roll a die once and flip a coin twice. Events are defined as follows: A = {Die is a 1} B = {Both flips of the coin are Tails}. Use this scenario to answer questions ) How many possible outcomes are there? 2) Give the sample space (Recommendation: use a table and let the columns of the table represent the outcomes when rolling the die and let the rows of the table represent the outcomes when flipping the coin twice). 3) Find P A 4) Find P B 5) Find P A 6) Find P Aand B 7) Find P A or B 8) Find P A B 9) Are events A and B mutually exclusive? 10) Are events A and B independent?

2 Use the Contingency Table above to answer questions Events are defined as follows: A = {Individual is Male} and B = {Individual weight is About Right} 11) Find 12) Find P A P B 13) Find P B 14) Find P B and A 15) Find P B or A 16) Find P B A 17) Are events A and B mutually exclusive? 18) Are events A and B independent? Suppose you have a bag with 5 red, 7 white, 3 blue poker chips. Use this information to answer questions ) If you draw four chips with replacement, what is the probability that all four are white? 20) If you draw four chips without replacement, what is the probability that all four are white? 21) If you draw four chips without replacement, what is the probability that at least one of the chips are not white?

3 Lab 7 Identifying Variable Frequencies Open the Student Survey Data. Create a Contingency Table for the variables Sport and Hand Select Analyze > Descriptive Statistics > Crosstabs. For the Row(s): choose Sport and for the Column(s): choose Hand. Click OK. Create a Contingency Table for the variables Eye and Travel Select Analyze > Descriptive Statistics > Crosstabs. For the Row(s): choose Eye and for the Column(s): choose Travel. Click OK. Create a Frequency Table for the variables Flip1-Flip10 and the variables Roll1-Roll10 Select Analyze > Descriptive Statistics > Frequencies. Under Variables(s): choose the variables Flip1-Flip10 and Roll1-Roll10 (there will be 20 variables so 20 tables will be created). To select all these variables at once click on Flip1, hold down shift key, click on Roll10, and then use the arrow to select them. Click OK.

4 SHORT ANSWER WRITING ASSIGNMENT 22) Use the Contingency Table created for the variables hand and sport to find the probabilities below. The events are defined as follows: A basketball is favorite sport and B left handed. a. b. c. d. P P A B P A P B e. P Aand B f. P A or B P A B g. h. P B A 23) Use the Contingency Table created for the variables hand and sport to answer the questions below. The events are defined as follows: A basketball is favorite sport and B left handed. a. Are events A and B mutually exclusive? Explain. b. Are events A and B dependent or independent? Explain. 24) Use the Contingency Table created for the variables eye and travel to find the probabilities below (when identified use probability rule to find probability). The events are defined as brown eyes B drive toschool. follows: A and a. P A b. P B c. Complement rule: P A d. Complement rule: P B e. P Aand B f. Addition rule: P A or B g. Conditional Probability rule: P A B h. Conditional Probability rule: P B A 25) Use the Contingency Table created for the variables eye and travel to answer the questions below. The events are defined as follows: A brown eyes and B drive toschool. a. Are events A and B mutually exclusive? Explain. b. Are events A and B dependent or independent? Explain.

5 26) Use the Frequency Tables for the variables Flip1-Flip10 to fill out the following table. In the last column of the table, calculate the probability of getting tails based on the frequency. Variable Number of Tails Number of Flips Probability of Tails Flip1 Flip2 Flip3 Flip4 Flip5 Flip6 Flip7 Flip8 Flip9 Flip10 27) Use the table created in question 26 for the following: a. If you flip a coin, what is the probability of getting tails (true probability not from table)? It is important to think about inferential statistics as we cover the topics included in the probability unit. In this situation the probability (same as proportion or percentage) of getting tails is like the parameter in a study. It is an exact value that we can only calculate by knowing the population. b. Explain why the probabilities calculated in the table are not all the same. In terms of inferential statistics, each probability from the table could be thought of as a statistic. The data was selected randomly because each time a coin was flipped a random outcome was selected. The probability (same as proportion or percentage) was then calculated. c. Explain why the probabilities calculated in the table are not equal to the true probability (part a above) of getting tails?

6 28) Use the Frequency Tables for the variables Roll1-Roll10 to fill out the following table. In the last column of the table, calculate the probability of getting a six based on the frequency. Variable Number of Sixes Number of Rolls Probability of a Six Roll1 Roll2 Roll3 Roll4 Roll5 Roll6 Roll7 Roll8 Roll9 Roll10 29) Use the table created in question 28 for the following: a. If you roll a die, what is the probability of getting a six (true probability not from table)? b. Explain how comparing the true probability of getting a six (part a above) to the above table is the same as what was illustrated in question 27 of this lab? c. What is different in this situation as compared to question 27 of this lab?