8% of all Americans suffer from sleep apnea. A researcher suspects that a higher percentage of those who live in the inner city have sleep apnea. Of the 367 people from the inner city surveyed, 37 of them suffered from sleep apnea. What can be concluded at the level of significance of α = 0.05?

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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8% of all Americans suffer from sleep apnea. A researcher suspects that a higher percentage of those who live in the inner city have sleep apnea. Of the 367 people from the inner city surveyed, 37 of them suffered from sleep apnea. What can be concluded at the level of significance of α = 0.05?

  1. Thus, the final conclusion is that ...
    • The data suggest the population proportion is not significantly larger than 8% at α = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 8%.
    • The data suggest the population proportion is not significantly larger than 8% at α = 0.05, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is larger than 8%.
    • The data suggest the populaton proportion is significantly larger than 8% at α = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is larger than 8%
  2. Interpret the p-value in the context of the study.
    • If the sample proportion of inner city residents who have sleep apnea is 10% and if another 367 inner city residents are surveyed then there would be a 7.08% chance of concluding that more than 8% of all inner city residents have sleep apnea.
    •  There is a 7.08% chance of a Type I error.
    • There is a 7.08% chance that more than 8% of all inner city residents have sleep apnea.
    • If the population proportion of inner city residents who have sleep apnea is 8% and if another 367 inner city residents are surveyed then there would be a 7.08% chance that more than 10% of the 367 inner city residents surveyed have sleep apnea.
  3. Interpret the level of significance in the context of the study.
    • If the population proportion of inner city residents who have sleep apnea is 8% and if another 367 inner city residents are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is larger than 8%.
    • There is a 5% chance that aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth.
    • If the population proportion of inner city residents who have sleep apnea is larger than 8% and if another 367 inner city residents are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is equal to 8%.
    • There is a 5% chance that the proportion of all inner city residents who have sleep apnea is larger than 8%.
8% of all Americans suffer from sleep apnea. A researcher suspects that a higher percentage of those who
live in the inner city have sleep apnea. Of the 367 people from the inner city surveyed, 37 of them suffered
from sleep apnea. What can be concluded at the level of significance of a =
0.05?
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
Select an answer ♥
(please enter a decimal)
H1:p v| Select an answer
(Please enter a decimal)
c. The test statistic ? v =
(please show your answer to 3 decimal places.)
d. The p-value
(Please show your answer to 4 decimal places.)
%3D
e. The p-value is ? va
f. Based on this, we should Select an answer v the null hypothesis.
g. Thus, the final conclusion is that ...
O The data suggest the population proportion is not significantly larger than 8% at a = 0.05, so
there is sufficient evidence to conclude that the population proportion of inner city residents
who have sleep apnea is equal to 8%.
O The data suggest the population proportion is not significantly larger than 8% at a = 0.05, so
there is not sufficient evidence to conclude that the population proportion of inner city
residents who have sleep apnea is larger than 8%.
%3D
The data suggest the populaton proportion is significantly larger than 8% at a = 0.05, so there
is sufficient evidence to conclude that the population proportion of inner city residents who
have sleep apnea is larger than 8%
h. Interpret the p-value in the context of the study.
O If the sample proportion of inner city residents who have sleep apnea is 10% and if another 367
inner city residents are surveyed then there would be a 7.08% chance of concluding that more
than 8% of all inner city residents have sleep apnea.
There is a 7.08% chance of a Type I error.
There is a 7.08% chance that more than 8% of all inner city residents have sleep apnea.
O If the population proportion of inner city residents who have sleep apnea is 8% and if another
367 inner city residents are surveyed then there would be a 7.08% chance that more than 10%
of the 367 inner city residents surveyed have sleep apnea.
i. Interpret the level of significance in the context of the study.
O If the population proportion of inner city residents who have sleep apnea is 8% and if another
367 inner city residents are surveyed then there would be a 5% chance that we would end up
falsely concluding that the proportion of all inner city residents who have sleep apnea is larger
than 8%.
There is a 5% chance that aliens have secretly taken over the earth and have cleverly disguised
themselves as the presidents of each of the countries on earth.
O If the population proportion of inner city residents who have sleep apnea is larger than 8% and
if another 367 inner city residents are surveyed then there would be a 5% chance that we
would end up falsely concluding that the proportion of all inner city residents who have sleep
apnea is equal to 8%.
O There is a 5% chance that the proportion of all inner city residents who have sleep apnea is
larger than 8%.
Transcribed Image Text:8% of all Americans suffer from sleep apnea. A researcher suspects that a higher percentage of those who live in the inner city have sleep apnea. Of the 367 people from the inner city surveyed, 37 of them suffered from sleep apnea. What can be concluded at the level of significance of a = 0.05? 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 Select an answer ♥ (please enter a decimal) H1:p v| Select an answer (Please enter a decimal) c. The test statistic ? v = (please show your answer to 3 decimal places.) d. The p-value (Please show your answer to 4 decimal places.) %3D e. The p-value is ? va f. Based on this, we should Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the population proportion is not significantly larger than 8% at a = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 8%. O The data suggest the population proportion is not significantly larger than 8% at a = 0.05, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is larger than 8%. %3D The data suggest the populaton proportion is significantly larger than 8% at a = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is larger than 8% h. Interpret the p-value in the context of the study. O If the sample proportion of inner city residents who have sleep apnea is 10% and if another 367 inner city residents are surveyed then there would be a 7.08% chance of concluding that more than 8% of all inner city residents have sleep apnea. There is a 7.08% chance of a Type I error. There is a 7.08% chance that more than 8% of all inner city residents have sleep apnea. O If the population proportion of inner city residents who have sleep apnea is 8% and if another 367 inner city residents are surveyed then there would be a 7.08% chance that more than 10% of the 367 inner city residents surveyed have sleep apnea. i. Interpret the level of significance in the context of the study. O If the population proportion of inner city residents who have sleep apnea is 8% and if another 367 inner city residents are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is larger than 8%. There is a 5% chance that aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth. O If the population proportion of inner city residents who have sleep apnea is larger than 8% and if another 367 inner city residents are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is equal to 8%. O There is a 5% chance that the proportion of all inner city residents who have sleep apnea is larger than 8%.
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