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Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of researchers is studying how combining compression bandages or compression hosiery with different types of footwear affects range of ankle motion. They suspect that more than half of all adults wearing compression bandages and no shoes will see decrease in range of ankle motion of at least 2° compared to when they are not wearing compression bandages or compression hosiery and are barefoot. They collect sample data from a random sample of 29 adults and determine that 17 see such a decrease in range of ankle motion. They compute a sample proportion of 17 = 0.586 %3D 29 The researchers conduct a one-sample z-test for a proportion, testing Ho : p = 0.500 against H1 : p > 0.500, where p is the proportion of adults whose range of angle motion decreases at least 2° while wearing compression bandages with no shoes. The lower limit of a 95% confidence interval for p is 0.436. Based on this interval, what should the researchers conclude about their z-test? The researchers should fail to reject Ho at a significance level of a = 0.10 - because || 0.586 > 0.436| a = 0.95 0.500 > 0.436 να=0. 10 v 0.586 > 0.436 0.586 > 0.500 a = 0.05

Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of researchers is studying how combining compression bandages or compression hosiery with different types of footwear affects range of ankle motion. They suspect that more than half of all adults wearing compression bandages and no shoes will see decrease in range of ankle motion of at least 2° compared to when they are not wearing compression bandages or compression hosiery and are barefoot. They collect sample data from a random sample of 29 adults and determine that 17 see such a decrease in range of ankle motion. They compute a sample proportion of 17 = 0.586 %3D 29 The researchers conduct a one-sample z-test for a proportion, testing Ho : p = 0.500 against H1 : p > 0.500, where p is the proportion of adults whose range of angle motion decreases at least 2° while wearing compression bandages with no shoes. The lower limit of a 95% confidence interval for p is 0.436. Based on this interval, what should the researchers conclude about their z-test? The researchers should fail to reject Ho at a significance level of a = 0.10 - because || 0.586 > 0.436| a = 0.95 0.500 > 0.436 να=0. 10 v 0.586 > 0.436 0.586 > 0.500 a = 0.05

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
Section10.3: Measures Of Spread
Problem 1GP
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Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of researchers is studying how combining compression bandages or compression hosiery with different types of footwear affects range of ankle motion. They suspect that more than half of all adults wearing compression bandages and no shoes will see a decrease in range of ankle motion of at least 2° compared to when they are not wearing compression bandages or compression hosiery and are barefoot. They collect sample data from a random sample of 29 adults and determine that 17 see such a decrease in range of ankle motion. They compute a sample proportion of 17 0.586 29 The researchers conduct a one-sample z-test for a proportion, testing Ho : p = 0.500 against H1 :p > 0.500, where p is the proportion of adults whose range of angle motion decreases at least 2° while wearing compression bandages with no shoes. The lower limit of a 95% confidence interval for p is 0.436. Based on this interval, what should the researchers conclude about their z-test? The researchers should fail to reject - Ho at a significance level of a = 0.10 because 0.586 > 0.436 a = 0.95 0.500 > 0.436 v a = 0.10 0.586 > 0.436 0.586 > 0.500 a = 0.05
Transcribed Image Text:Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of researchers is studying how combining compression bandages or compression hosiery with different types of footwear affects range of ankle motion. They suspect that more than half of all adults wearing compression bandages and no shoes will see a decrease in range of ankle motion of at least 2° compared to when they are not wearing compression bandages or compression hosiery and are barefoot. They collect sample data from a random sample of 29 adults and determine that 17 see such a decrease in range of ankle motion. They compute a sample proportion of 17 0.586 29 The researchers conduct a one-sample z-test for a proportion, testing Ho : p = 0.500 against H1 :p > 0.500, where p is the proportion of adults whose range of angle motion decreases at least 2° while wearing compression bandages with no shoes. The lower limit of a 95% confidence interval for p is 0.436. Based on this interval, what should the researchers conclude about their z-test? The researchers should fail to reject - Ho at a significance level of a = 0.10 because 0.586 > 0.436 a = 0.95 0.500 > 0.436 v a = 0.10 0.586 > 0.436 0.586 > 0.500 a = 0.05
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