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Problem Solving and Data Analysis 13 – Data Inferences Calculator Required Day 1 Entrance Slip Discussion 1. A teacher wants to find the average height, in cm, of her seventh hour students. Is this a feasible measurement to obtain? Justify your answer. Yes, this information can be obtained. She can simply measure all the students and average the heights. 2. A superintendent wants to find the average number of AP/Honors classes each student in the district is currently taking. Is this a feasible measurement to obtain? Justify your answer. Yes, this information can be obtained. The school district can run a report on AP/Honors classes and computer the average. 3. A large shoe company wants to know the average shoe size for every person currently living in the United States. If this a feasible measurement to obtain? Justify your answer. No, this information cannot be obtained. There are too many people to contact and such a project would be too expensive. Because some information cannot be obtained, researchers will approximate the larger group using a smaller sample. When researchers cannot find the exact value and need to estimate using the results from a smaller sample, there is some wiggle-room for the approximations. We call this wiggle-room the Margin of Error. A large shoe company wants to know the average shoe size for every person currently living in the United States. To approximate this value, the company randomly selects 10,000 US residents and records their shoe size. The average shoe size recorded is 9.7 with a margin of error of 1.1 at the 95% confidence level. What they want to know (parameter) Who they want to know about (population) What value they found (statistic) Wiggle-room (Marin of Error) Who they ask (sample) The shoe company can estimate that the average for all people living in the US is: 9.7 1.1 Writing it like this can be confusing. Results are often given as a confidence interval. The company estimates the average shoe size of people living in the United States to be between 8.6 and 10.8. In a poll of 1,578 randomly selected American adults, 44.8% of the respondents said that airlines should allow in-flight calls on airplanes. The poll reported a margin of error of 2.5% at a 95% confidence level. 1. What is the value obtained through sampling (sample statistic)? 2. What is the margin of error? 44.8% 2.5% 3. Between which two values could the actual percentage for all American adults fall (confidence interval)? Between 42.3% and 47.3% 4. Select all that apply. Which of the following could be equal to the percentage of all American adults who say that airlines should allow in-flight calls? A. 40% B. 43% C. 45% D. 48% E. 95% Based on random samples of river heights, oceanographers estimate that 4,800 3 cubic kilometers km of freshwater is discharged into the Arctic Ocean annually. The estimate has a margin of error of 240km3 at the 90% confidence level. Which of the following is the most reasonable claim about the volume of freshwater discharged annually into the Arctic Ocean? A. It is between 4,800 and 5,040 cubic km. B. It is between 4,560 and 5,040 cubic km. C. It is between 240 and 4,800 cubic km. D. It is between 240 and 4,320 cubic km. 4800 – 240 = 4560 4800 + 240 = 5040 Prior to the 2014 elections, 1,000 randomly selected Louisiana voters were surveyed about what single issue would most likely influence their vote. Of those surveyed, 560 voters answered that the state of the economy would most influence their vote. Based on this information, which statement about all voters in Louisiana is most appropriate? Estimation, not exact. A. Exactly 56% of all Louisiana voters thought the state of the economy would most influence their voting. B. Approximately 56% of all Louisiana voters thought the state of the economy would most influence their voting. Exactly what they answered. C. Exactly 56% of Louisiana voters would vote for the candidate with the best plan to improve the economy. D. Approximately 56% of Louisiana voters would vote for the candidate with the best plan to improve the economy. “Best plan” is subjective. A random sample of 500 residents of a town included 173 residents who primarily spoke a language other than English at home, with a margin of error of 25 residents and a confidence level of 98%. If the town has 25,000 residents, how many residents primarily speak a language other than English at home, with a 98% confidence level? 173 Sample Statistic = 34.6% A. 7,400 to 9,900 residents 500 25 Margin of Error = 5% 500 B. 8,625 to 8,675 residents Confidence Interval with % = (29.6%, 39.6%) Confidence Interval with residents = (7400, 9900) C. 24,475 to 24,525 residents D. 23,250 to 25,750 residents