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13% of all Americans suffer from sleep apnea. A researcher suspects that a lower percentage of those who live in the inner city have sleep apnea. Of the 338 people from the inner city surveyed, 37 of them suffered from sleep apnea. What can be concluded at the level of significance of a = 0.10?

13% of all Americans suffer from sleep apnea. A researcher suspects that a lower percentage of those who live in the inner city have sleep apnea. Of the 338 people from the inner city surveyed, 37 of them suffered from sleep apnea. What can be concluded at the level of significance of a = 0.10?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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topic is Hypothesis test for proportions.

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13% of all Americans suffer from sleep apnea. A researcher suspects that a lower percentage of those who live in the inner city have sleep apnea. Of the 338 people from the inner city surveyed, 37 of them suffered from sleep apnea. What can be concluded at the level of significance of a = 0.10? a. For this study, we should use z-test for a population proportion v b. The null and alternative hypotheses would be: Ho: p v (please enter a decimal) = H1: p v> (Please enter a decimal) c. The test statistic z v (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is > va f. Based on this, we should (fail to reject v the null hypothesis. g. Thus, the final conclusion is that O The data suggest the population proportion is not significantly smaller than 13% at a = 0.10, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 13%. O The data suggest the populaton proportion is significantly smaller than 13% at a = 0.10, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 13% O The data suggest the population proportion is not significantly smaller than 13% at a = 0.10, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 13%. h. Interpret the p-value in the context of the study. There is a 13% chance of a Type I error O If the population proportion of inner city residents who have sleep apnea is 13% and if another 338 inner city residents are surveyed then there would be a 13.08% chance fewer than 11% of the 338 residents surveyed have sleep apnea. O If the sample proportion of inner city residents who have sleep apnea is 11% and if another 338 inner city residents are surveyed then there would be a 13.08% chance of concluding that fewer than 13% of inner city residents have sleep apnea. O There is a 13.08% chance that fewer than 13% of all inner city residents have sleep apnea. i. Interpret the level of significance in the context of the study. O There is a 10% chance that the proportion of all inner city residents who have sleep apnea is smaller than 13%. O If the population proportion of inner city residents who have sleep apnea is smaller than 13% and if another 338 inner city residents are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is equal to 13%. O If the population proportion of inner city residents who have sleep apnea is 13% and if another 338 inner city residents are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is smaller than 13%. O There is a 10% chance that aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth.
Transcribed Image Text:13% of all Americans suffer from sleep apnea. A researcher suspects that a lower percentage of those who live in the inner city have sleep apnea. Of the 338 people from the inner city surveyed, 37 of them suffered from sleep apnea. What can be concluded at the level of significance of a = 0.10? a. For this study, we should use z-test for a population proportion v b. The null and alternative hypotheses would be: Ho: p v (please enter a decimal) = H1: p v> (Please enter a decimal) c. The test statistic z v (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is > va f. Based on this, we should (fail to reject v the null hypothesis. g. Thus, the final conclusion is that O The data suggest the population proportion is not significantly smaller than 13% at a = 0.10, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 13%. O The data suggest the populaton proportion is significantly smaller than 13% at a = 0.10, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 13% O The data suggest the population proportion is not significantly smaller than 13% at a = 0.10, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 13%. h. Interpret the p-value in the context of the study. There is a 13% chance of a Type I error O If the population proportion of inner city residents who have sleep apnea is 13% and if another 338 inner city residents are surveyed then there would be a 13.08% chance fewer than 11% of the 338 residents surveyed have sleep apnea. O If the sample proportion of inner city residents who have sleep apnea is 11% and if another 338 inner city residents are surveyed then there would be a 13.08% chance of concluding that fewer than 13% of inner city residents have sleep apnea. O There is a 13.08% chance that fewer than 13% of all inner city residents have sleep apnea. i. Interpret the level of significance in the context of the study. O There is a 10% chance that the proportion of all inner city residents who have sleep apnea is smaller than 13%. O If the population proportion of inner city residents who have sleep apnea is smaller than 13% and if another 338 inner city residents are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is equal to 13%. O If the population proportion of inner city residents who have sleep apnea is 13% and if another 338 inner city residents are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is smaller than 13%. O There is a 10% chance that aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth.
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