Answered: 13% of all Americans suffer from sleep…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Question

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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 303 people from the inner city surveyed, 36 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.01?

For this study, we should use
The null and alternative hypotheses would be:
Ho: (please enter a decimal)
H₁: (Please enter a decimal)

The test statistic = (please show your answer to 3 decimal places

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Follow-up Question

The p-value = (Please show your answer to 4 decimal places.)
The p-value is < or > α
Based on this, we should the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the populaton proportion is significantly smaller than 13% at αα = 0.01, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 13%
- The data suggest the population proportion is not significantly smaller than 13% at αα = 0.01, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 13%.
- The data suggest the population proportion is not significantly smaller than 13% at αα = 0.01, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 13%.
Interpret the p-value in the context of the study.
- There is a 28.13% chance that fewer than 13% of all inner city residents have sleep apnea.
- If the sample proportion of inner city residents who have sleep apnea is 12% and if another 303 inner city residents are surveyed then there would be a 28.13% chance of concluding that fewer than 13% of inner city residents have sleep apnea.
- There is a 13% chance of a Type I error
- If the population proportion of inner city residents who have sleep apnea is 13% and if another 303 inner city residents are surveyed then there would be a 28.13% chance fewer than 12% of the 303 residents surveyed have sleep apnea.
Interpret the level of significance in the context of the study.
- There is a 1% chance that aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth.
- There is a 1% chance that the proportion of all inner city residents who have sleep apnea is smaller than 13%.
- If the population proportion of inner city residents who have sleep apnea is 13% and if another 303 inner city residents are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is smaller than 13%.
- If the population proportion of inner city residents who have sleep apnea is smaller than 13% and if another 303 inner city residents are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is equal to 13%.