Name: Block: Date: Applications Students

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1 Name: Block: Date: 7.SP.2 Using Data from a Random Sample Problem Bank 1. Below is the data collected from a random sample of 100 graduating seniors on the number of college applications they submitted in their senior year. What inferences would you draw about the senior class as a whole? Applications Students Ms. Gordon has not had the time to grade every students' test, but she wants to get a general sense of how her students did. Ms. Gordon shuffles her papers, picks 10 papers at random and grades them, yielding the results below. What inferences would you draw about the performance of Ms. Gordon's students? A B C Selena Gomez is reading an article about America's favorite desserts, which includes the table below. Selena Gomez turns to you and says, "I always loved popsicles. Looks like they're America's favorite as well." What would you say to Selena Gomez? Total Popsicles Ice Cream Pie Cheese Total

2 4. In his second term, President Obama hires Lindsay Lohan as a fashion analyst. At the President's request, Lindsay Lohan conducts a survey of American necktie preferences. She asks her two assistants to poll 100 shoppers each in the men s wear department at Bloomingdale s and Macy s. When Lindsay Lohan reports to President Obama, she says, "Red ties show the most support, with about 39% of the vote." Where is Lindsay Lohan getting her numbers? Do you agree? Assistant 1 Assistant 2 Red Blue Piano Key No Tie Total Gallup is polling American teenagers on the most admirable celebrities. Gallup conducts two random surveys of 100 people. After the surveys are complete, they combine the two surveys into one data set of 200 people, yielding the results below. (a) Which column of the table is the most representative of American teenagers as a whole? Explain. (b) What conclusions can you draw from the data collected? Combined Rihanna Miley Cyrus Emma Watson Kendrick Lamar Total

3 6. Two research teams are investigating water quality in the Charles River. Azealia Banks Research collects two samples with 100 measurements in each sample. Andrew Luck Research collects two samples with 50 measurements in each sample. (a) Which team's estimate would you expect to be more representative? Why? (b) Which pair of samples would you expect to show less variation? Explain. 7. President Obama is trying to decide what to focus on in his second term, so he hires a polling firm to conduct a random sample of American adults. At Michelle's suggestion, he then hires a second firm so that he can compare the samples. The firms conduct the surveys and present the following results: Firm 1 Firm 2 Gun Control 27,000 27,000 Immigration 30,000 24,000 Debt Reduction 8,000 9,000 Counter Terrorism 10,000 9,000 Education 25,000 31,000 Total 100, ,000 (a) Based only on sample 1, what issue(s) would you recommend President Obama prioritize? Why? (b) Based only on sample 2? (c) Based on both samples? 8. Beyonce and Azealia Banks are at a party with a giant bowl of M&M's. They aren't really enjoying the conversation, so they decide to entertain themselves by arguing about the ratios between the different colors of M&M's. To resolve their argument, Beyonce and Azealia Banks start taking random samples from the bowl. Beyonce samples ten at a time, and Azealia Banks samples fifty at a time. (a) Whose samples would you expect to show more variation? Explain. (b) Suppose that Beyonce collects twenty samples of ten, and Azealia Banks collects four samples of fifty. Then, each of them puts their two hundred M&M's in a bowl. Which of these bowls of two hundred M&M's is more representative of the giant bowl?

4 9. Drake is working in marketing at Apple, and he is interested in why people are buying the iphone 5. He decides to take a random sample of iphone 5 users, yielding the following results: Thinner Bigger Screen Better Camera Status Symbol 2 4 Speed Total a. What are the most striking examples of variation between samples? b. For the categories that show notable variation, what value would you expect to see in a perfectly representative sample of the same size? c. How should Drake summarize the data in an to his co- workers? 10. Kylie is an engineer working on smartphone batteries for Samsung, and she is interested in the real-life battery performance of the Samsung Galaxy. She secretly installs software on a random sample of Galaxy phones that will send her information on battery performance. After several weeks, she has collected the data below. 3-4 hours hours hours hours a. What are the most striking examples of variation between the samples? b. For the categories that display substantial variation, what value would you expect to see in a perfectly representative sample of the same size? c. How might Kylie summarize the data?

5 11. Winterland Academy uses a software program that tracks the websites visited by its employees. Below is a breakdown of the most popular websites during two randomly selected school days. What inferences would you draw about Winterland teachers web surfing habits? Google NY Times Pinterest Facebook ESPN Day Day Total Jennifer Lawrence is working at a website, and she is trying to decide which feature will bring users the most joy. She conducts two random samples of users and collects the information into the table below. Mobile Version Share on Facebook 9 12 Advanced Search 10 9 Personalized Suggestions Total a. Describe the variation between the samples. b. How should Jennifer Lawrence prioritize the listed features?