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Math 80 - Statistics Central Limit Theorem for Sample Proportions Handout 5.1 GROUP WORK U.S. schools face an ongoing challenge: as students get closer to high school graduation, their enthusiasm for school falls. A Gallup poll in June 2017 has discovered that fifth graders are most engaged with school, while 11th graders are least. The latest Gallup poll showed that only 32% of 11th graders are engaged in school. Assume this value represents the population proportion. Suppose we randomly sample 180 11th graders in the U.S., and ask them about their engagement in school. a). Find the mean, μp, and standard error, σp, of the resulting sampling distribution of sample proportions of size 180. Based on the mean and standard error, label the values of a through g on the normal curve on the right. The values are one standard deviation apart. a b C d e f f g b). What does this sampling distribution represent? c). Use the empirical rule to find the interval centered at p that contains approximately 99.7% of all p. PE d). In a random sample of 180 11th graders in the U.S., only 25.7% say they are engaged in school. Is this sample proportion unusual? Use technology to find the probability that 25.7% or less in a sample of 180 11th graders will say they are engaged in school. Write probability notation. e). In another random sample of 180 11th graders, 78 say they are engaged with their school work. Is this sample proportion unusual? Find the probability that among a random sample of 180 11th graders, 78 or more will say they are engaged in school. Write probability notation. Give your answer in percentage. STATWAYTM STUDENT HANDOUT PAGE 6

Math 80 - Statistics Central Limit Theorem for Sample Proportions Handout 5.1 GROUP WORK U.S. schools face an ongoing challenge: as students get closer to high school graduation, their enthusiasm for school falls. A Gallup poll in June 2017 has discovered that fifth graders are most engaged with school, while 11th graders are least. The latest Gallup poll showed that only 32% of 11th graders are engaged in school. Assume this value represents the population proportion. Suppose we randomly sample 180 11th graders in the U.S., and ask them about their engagement in school. a). Find the mean, μp, and standard error, σp, of the resulting sampling distribution of sample proportions of size 180. Based on the mean and standard error, label the values of a through g on the normal curve on the right. The values are one standard deviation apart. a b C d e f f g b). What does this sampling distribution represent? c). Use the empirical rule to find the interval centered at p that contains approximately 99.7% of all p. PE d). In a random sample of 180 11th graders in the U.S., only 25.7% say they are engaged in school. Is this sample proportion unusual? Use technology to find the probability that 25.7% or less in a sample of 180 11th graders will say they are engaged in school. Write probability notation. e). In another random sample of 180 11th graders, 78 say they are engaged with their school work. Is this sample proportion unusual? Find the probability that among a random sample of 180 11th graders, 78 or more will say they are engaged in school. Write probability notation. Give your answer in percentage. STATWAYTM STUDENT HANDOUT PAGE 6

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Math 80 - Statistics Central Limit Theorem for Sample Proportions Handout 5.1 GROUP WORK U.S. schools face an ongoing challenge: as students get closer to high school graduation, their enthusiasm for school falls. A Gallup poll in June 2017 has discovered that fifth graders are most engaged with school, while 11th graders are least. The latest Gallup poll showed that only 32% of 11th graders are engaged in school. Assume this value represents the population proportion. Suppose we randomly sample 180 11th graders in the U.S., and ask them about their engagement in school. a). Find the mean, μp, and standard error, σp, of the resulting sampling distribution of sample proportions of size 180. Based on the mean and standard error, label the values of a through g on the normal curve on the right. The values are one standard deviation apart. a b C d e f f g b). What does this sampling distribution represent? c). Use the empirical rule to find the interval centered at p that contains approximately 99.7% of all p. PE d). In a random sample of 180 11th graders in the U.S., only 25.7% say they are engaged in school. Is this sample proportion unusual? Use technology to find the probability that 25.7% or less in a sample of 180 11th graders will say they are engaged in school. Write probability notation. e). In another random sample of 180 11th graders, 78 say they are engaged with their school work. Is this sample proportion unusual? Find the probability that among a random sample of 180 11th graders, 78 or more will say they are engaged in school. Write probability notation. Give your answer in percentage. STATWAYTM STUDENT HANDOUT PAGE 6
Transcribed Image Text:Math 80 - Statistics Central Limit Theorem for Sample Proportions Handout 5.1 GROUP WORK U.S. schools face an ongoing challenge: as students get closer to high school graduation, their enthusiasm for school falls. A Gallup poll in June 2017 has discovered that fifth graders are most engaged with school, while 11th graders are least. The latest Gallup poll showed that only 32% of 11th graders are engaged in school. Assume this value represents the population proportion. Suppose we randomly sample 180 11th graders in the U.S., and ask them about their engagement in school. a). Find the mean, μp, and standard error, σp, of the resulting sampling distribution of sample proportions of size 180. Based on the mean and standard error, label the values of a through g on the normal curve on the right. The values are one standard deviation apart. a b C d e f f g b). What does this sampling distribution represent? c). Use the empirical rule to find the interval centered at p that contains approximately 99.7% of all p. PE d). In a random sample of 180 11th graders in the U.S., only 25.7% say they are engaged in school. Is this sample proportion unusual? Use technology to find the probability that 25.7% or less in a sample of 180 11th graders will say they are engaged in school. Write probability notation. e). In another random sample of 180 11th graders, 78 say they are engaged with their school work. Is this sample proportion unusual? Find the probability that among a random sample of 180 11th graders, 78 or more will say they are engaged in school. Write probability notation. Give your answer in percentage. STATWAYTM STUDENT HANDOUT PAGE 6
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