Lab 2 Pre-Lab and Exercises (1)

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9/11/2019 Statistics 213 Lab Exercises – Probability 2 https://scott-robison.rstudio.cloud/a8c401512bf9446cb9e30f29e3a95885/file_show?path=%2Fcloud%2Fproject%2FLab2.html 1/7 Statistics 213 Lab Exercises – Probability 2 © Jim Stallard, Scott Robison, and Claudia Mahler 2019 all rights reserved. Pre-Lab Exercise: A poll conducted in 2015 found that 85% of Canadians support the decriminalization/legalization of recreational use of marijuana, where as 15% said recreational marijuana usage should be criminalized. Thirty percent (30%) of Canadians surveyed in this poll preferred the NDP party over other political parties. Of all Canadians surveyed, 27% support the decriminalization/legalization of recreational marijuana usage and indicated a preference for the NDP party. Perhaps if we organize the information we have been given we will be able to know more about the information we have not been given. Using a table with both rows and columns (a two-way-table) to represent the two variables ( and ) may prove useful in calculating information that is not directly given to us. Party marijuana_usage non_marijuana_usage totals NDP 0.27 0.3 not NDP totals 0.85 0.15 I hope the table makes filling in the blanks seem intuitive. Rows should add to their totals and so should columns. So…let’s fill the information in!

9/11/2019 Statistics 213 Lab Exercises – Probability 2 https://scott-robison.rstudio.cloud/a8c401512bf9446cb9e30f29e3a95885/file_show?path=%2Fcloud%2Fproject%2FLab2.html 2/7 Party marijuana_usage non_marijuana_usage totals Party marijuana_usage non_marijuana_usage totals NDP 0.27 0.03 0.3 not NDP 0.58 0.12 0.7 totals 0.85 0.15 1.0 a. From the information provided, can you say that a Canadian’s view about the decriminalization/legalization of marijuana usage and their preference for NDP party are independent events? Make sure you use probability theory to justify your answer. We know/have seen that if two events and are independent, then , and if then and are not independent (dependent)! From the filled in table above, we see and . Use as a calculator: 0.3*0.85 ## [1] 0.255 Therefore, if , then are independent. However, reading from the table, we can see that . So we know are dependent . Try, using this method, to determine if are independent events. b. As a follow up to part (a), can you say that a Canadian’s view about the decriminalization/legalization of marijuana usage and their preference for the NDP party are mutually exclusive events? Again, make sure your answer is justified with probability. The two events can only be mutually exclusive if the .

9/11/2019 Statistics 213 Lab Exercises – Probability 2 https://scott-robison.rstudio.cloud/a8c401512bf9446cb9e30f29e3a95885/file_show?path=%2Fcloud%2Fproject%2FLab2.html 3/7 c. Suppose you are to randomly pick a Canadian and ask them the following questions to answer the following statements. 1. In Canada, the recreational use of marijuana should be ___________. (Possible responses: 1. decriminalized/legalized OR 2. criminalized) 2. In Canada, what political party to you prefer? (Possible responses: 1. Conservative 2. Liberal 3. NDP 4. Green 5. BQ (Bloc Quebecois)) Find the probability that this person responds “decriminalization/legalized” and “does not prefer the NDP party.” Again, reference the table: Party marijuana_usage non_marijuana_usage totals NDP 0.27 0.03 0.3 not NDP 0.58 0.12 0.7 totals 0.85 0.15 1.0 The probability of the intersection of “not NDP” and “marijuana_usage” is so it cannot be mutually exclusive. In fact it appears quite likely with a probability of . d. Suppose the person in part (c) responded “NDP Party.”What is the probability this person’s response to Question 1 was “decriminalization/legalization?” Here we have something new going on. We are “conditioning” our results. Instead of holding interest in a person’s response to legalization, we are suggesting to only consider those who support the NDP and then inquiring their opinion regarding legalization. This conditioning is written using this notation: Use as a calculator: 0.27/0.3 ## [1] 0.9

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9/11/2019 Statistics 213 Lab Exercises – Probability 2 https://scott-robison.rstudio.cloud/a8c401512bf9446cb9e30f29e3a95885/file_show?path=%2Fcloud%2Fproject%2FLab2.html 4/7 e. As a follow up to part (d), what is the probability the person’s response to Question 1 was not “decriminalization,” again given they support the NDP? Use as a calculator: 0.03/0.3 ## [1] 0.1 f. Suppose this person’s response to Question 2 was a political party that was not the NDP. Find the probability that this person responded “criminalize” to Question 1. Use as a calculator: 0.12/0.7 ## [1] 0.1714286 Lab Exercise 1: A random experiment produces many possible events. Two of these events are event ? and event ? . These events are independent of each other and occur with and . Event B not_B totals A 0.4 not_A totals 0.73 1

9/11/2019 Statistics 213 Lab Exercises – Probability 2 https://scott-robison.rstudio.cloud/a8c401512bf9446cb9e30f29e3a95885/file_show?path=%2Fcloud%2Fproject%2FLab2.html 5/7 a. Find . Remember in this question that and are independent, so here, Add your result to the table. Once you’ve done so, you should be able to complete the rest of the table and answer the remaining questions. b. Find . c. Find the probability of neither event nor event occurring: . d. Find the probability of exactly one of these two events occurring. Be careful; exactly one of two . Instead it is . Lab Exercise 2: Two different events and exist, where and . Moreover, and are mutually exclusive events, so . A student currently taking Statistics 213 determines from this that “ and are independent events.” Is this student correct? Why or why not? Notice that the statement implies that since the question did not state . So if (and for the same reason) is it possible for , while and are independent? Lab Exercise 3: A recent survey on Canadian firearms regulations suggested that 71.4% of Canadians supported stronger gun laws, while 28.6% believe that current gun laws are strong enough and do not need strengthening. In addition, 54.58% of males support stronger gun laws in Canada while 87.62% of females support stronger gun laws. Assume 50.9% of Canadians are female. A Canadian resident is randomly picked.

9/11/2019 Statistics 213 Lab Exercises – Probability 2 https://scott-robison.rstudio.cloud/a8c401512bf9446cb9e30f29e3a95885/file_show?path=%2Fcloud%2Fproject%2FLab2.html 6/7 Event StrongerGunLaws not_StrongerGunLaws totals Female 0.509 not_Female totals 0.714 0.286 1 There is also some other information given that we must carefully consider. “In addition, 54.58% of males support stronger gun laws in Canada while 87.62% of females support stronger gun laws.” As I carefully consider the statement “54.58% of males support stronger gun laws,” I have realized it really means “out of the men, 54.58% support stronger gun laws.” . We also know that , so we can sub in what we know and solve for what we don’t. Use as a calculator: 0.5458*(1-0.509) ## [1] 0.2679878 Now, you can carefully consider what the statement “87.62% of females support stronger gun laws” means and how you can “convert” this information into something you can insert into your table. a. Find the probability the randomly selected person is a female and supports stronger gun laws. That is, find . b. Suppose the selected person does not support stronger gun laws. Find the probability this person is female. That is, find .

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9/11/2019 Statistics 213 Lab Exercises – Probability 2 https://scott-robison.rstudio.cloud/a8c401512bf9446cb9e30f29e3a95885/file_show?path=%2Fcloud%2Fproject%2FLab2.html 7/7 c. If this randomly chosen person does support stronger gun laws, what is the probability this person is male? Find . d. From this information, can you say that “sex” and “support stronger gun laws” are independent events? Can you say these are mutually exclusive events? Make sure you use probability in your answer. Use the skills you have learned in this lab to complete the lab quiz.