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Lesson 8.2.2 – Teacher Notes • Standard: • 7.SP.A.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. • 7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade book. • Full mastery can be expected by the end of the chapter. • Lesson Focus: • The focus of the lesson is for students to use data, plot on a dot plot, and compare data while making inferences. In order to provide students exposure to dot plots, the resource page needs to be adjusted to include smaller numbers with a closer range. The questions in the text can all still be used but problem 8-42 needs to be changed to incorporate creating a dot plot. (8-42 and 8-43) • I can draw informal comparative inferences about two populations from random samples. • Calculator: Yes • Literacy/Teaching Strategy: Teammates Consult (8-41); Walk and Talk (Closure)
http://juiceboxinteractive.com/ideas/pepsi-lost-challenge-won-battle/http://juiceboxinteractive.com/ideas/pepsi-lost-challenge-won-battle/
NO The sample did not include teenagers.
8-43. Cyrus plays volleyball in county-wide tournaments. He wondered what portion of volleyball players prefer plain water over sports drinks during intense games. • At his next tournament, Cyrus selected 50 random players from all the teams to ask about their preference. 78% preferred plain water. What inference can Cyrus make about all the volleyball players in the county? • What additional information would Cyrus • gain if it was practical to take many samples • at many tournaments in the county? 78% prefer plain water Get a larger sample that would be more accurate.
8-43. Cyrus plays volleyball in county-wide tournaments. He wondered what portion of volleyball players prefer plain water over sports drinks during intense games. • If many samples could be taken, the distribution of percentages in each of the samples might look like this:% preferring water: • 84% 71% 73% 83% 80% 80% 79% 77% 81% 72% 81% 78% • Make a box plot of the sample means. With this additional information, make a new statement about volleyball players and water. 71%, 72%, 73%,77%, 78%, 79%, 80%, 80%, 81%, 81%, 83%, 84% 79.5 84 71 75 81
Practice • Here are two dot plots. Students were surveyed and asked what they thought their grade would be on a math exam. The results of the survey are in green. Then the students took the math test and the scores were plotted on the top graph in purple. The blue line is the halfway point between the scores. List 4 inferences you can make based upon the dot plots. 1.The median of the actual scores is higher. 2.The actual scores are more skewed to the right. 3.The actual scores data is bell shaped. 4.The predicated scores’ median is 12. 5.The students did better than was predicted.
Practice 2. The figures to the right show the female life expectancies for countries of Africa and Europe. List 4 inferences you can make based upon the box-and-whiskers plot. 1.African females’ life span is more spread out than the European Female. 2.European Female’s life expectancy is higher. 3.European Females’ life median is higher. 4.African Females maximum is the same as European’s median.
Practice 2. The figures to the right show the female life expectancies for countries of Africa and Europe. List 2 DIFFERENT inferences you can make based upon the dot plot. 1.African females life span is more spread out than the European Female. AF dot plot is skewed to the Right. 2.European Female life expectancy is higher than the African Females life span. (EF dot plot has 2 peaks)
