Two Way Table. FB vs Twitter and Covid

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Napa Valley College *

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232

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Statistics

Date

Jan 9, 2024

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pdf

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Uploaded by MajorMaskSnake30

Let’s consider two popular social media platforms, Facebook and Twitter. Random variables could be assigned as follows: Var 1 = Twitter Usage; with Possible values of Twitter and No Twitter Var 2 = Facebook Usage; with Possible values of Facebook and No Facebook Each of the variables is a qualitative variable with two possible values. The corresponding Two-Way Table setup is shown below. Twitter No Twitter Facebook Totals Facebook A B C No Facebook D E F Twitter Totals G H I The following probabilities apply to randomly selecting an individual in the 18 – 29 age group, in 2021. The 18 – 29 age group is not another variable, rather, this will be our population. P(Facebook) 1 = 0.95 P(Twitter) 2 = 0.42 We will use these probabilities to populate the Two-Way Table with counts. The boxes in a Two-Way Table always contain counts . We can assume any population size we want for these types of applications. Starting with large numbers makes it less likely we will have decimals in the table. 1. For the sake of continuity, let’s all use a value of 1,000,000 to fill in this box. Which box will we use to record our hypothetical population size? (Possible Answers include: A, B, C, D, E, F, G, H, I ) 1 https://www.pewresearch.org/internet/2021/04/07/social-media-use-in- 2021/#:~:text=Fully%2095%25%20of%20those%2018,Americans%20are%20narrower%20for%20Facebook. 2 https://www.statista.com/statistics/265647/share-of-us-internet-users-who-use-twitter-by-age- group/#:~:text=In%20February%202021%2C%20it%20was,to%2049%2Dyear%2Dolds.

P(Facebook) = 0.95 P(Twitter) = 0.42 2. Next, we use the given marginal probabilities (repeated above) to fill in all the counts in the margins. a. Count in box C = b. Count in box F = c. Count in box G = d. Count in box H = To fill in the remaining boxes, we will need to be given a Conditional Probability. Suppose that the probability that a user of Twitter uses Facebook is 0.96. (Note, do you see in the wording here that the condition, the thing we know is true, is that the individual is a user of Twitter. And out of those users of Twitter, the probability that someone uses Facebook is 0.96) 3. While using this conditional probability to fill in a box, to which column or row does the conditional probability restrict our view? (i.e. Do we look only at the Twitter column or only at the Facebook row?) 4. Use the conditional probability to fill in the appropriate box, and all find counts for the remaining boxes. a. Count in box A = b. Count in box B = c. Count in box D = d. Count in box E = Twitter No Twitter Facebook Totals Facebook A B C No Facebook D E F Twitter Totals G H I

The data below was used to construct the Two-Way Table that follows. • The US Census Bureau 2019 report gave the following with regard to Napa County population: § 51.8% identified themselves as White § 35% identified themselves as Latino • An article in the Napa Valley Register on March 23, 2021 reports the following: § 26.1% of Napa County Residents have been vaccinated. § 41% of those that have received at least one dose of a Covid-19 vaccine are White. § 12.1% of those that have received at least one dose of a Covid-19 vaccine are Latino. Has Received at least one dose of a Covid-19 Vaccine Has NOT Received at least one dose of a Covid-19 Vaccine Race Totals Identified as White 107,010 410,990 518,000 Identified as Latino 31,581 318,419 350,000 Other 122,409 9,591 132,000 Vaccine Totals 261,000 739,000 1,000,000 5. What is the probability that someone who identifies as White has received at least one dose of a Covid-19 Vaccine? 6. What is the probability that someone who identifies as Latino has received at least one dose of a Covid-19 Vaccine? 7. Is the probability of someone having received at least one dose of a Covid-19 Vaccine independent of the variable Race? Explain why or why not using your calculations as reasoning.

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