14% 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 359 people from the inner city surveyed, 43 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.05? For this study, we should use Select an answer z-test for a population proportion t-test for a population mean  The null and alternative hypotheses would be:      Ho: ? μ p  Select an answer = ≠ > <   (please enter a decimal)     H1: ? p μ  Select an answer < > = ≠   (Please enter a decimal) The test statistic ? t z  =  (please show your answer to 3 decimal places.) The p-value =  (Please show your answer to 4 decimal places.) The p-value is ? > ≤  αα Based on this, we should Select an answer reject fail to reject accept  the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton proportion is significantly smaller than 14% at αα = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 14% The data suggest the population proportion is not significantly smaller than 14% at αα = 0.05, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 14%. The data suggest the population proportion is not significantly smaller than 14% at αα = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 14%. Interpret the p-value in the context of the study. If the sample proportion of inner city residents who have sleep apnea is 12% and if another 359 inner city residents are surveyed then there would be a 13.47% chance of concluding that fewer than 14% of inner city residents have sleep apnea.  There is a 14% chance of a Type I error If the population proportion of inner city residents who have sleep apnea is 14% and if another 359 inner city residents are surveyed then there would be a 13.47% chance fewer than 12% of the 359 residents surveyed have sleep apnea. There is a 13.47% chance that fewer than 14% of all inner city residents have sleep apnea. Interpret the level of significance in the context of the study. If the population proportion of inner city residents who have sleep apnea is smaller than 14% and if another 359 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 14%. There is a 5% chance that the proportion of all inner city residents who have sleep apnea is smaller than 14%. 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 14% and if another 359 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 smaller than 14%.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

14% 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 359 people from the inner city surveyed, 43 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.05?

  1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean 
  2. The null and alternative hypotheses would be:    
     Ho: ? μ p  Select an answer = ≠ > <   (please enter a decimal)   
     H1: ? p μ  Select an answer < > = ≠   (Please enter a decimal)
  1. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
  2. The p-value =  (Please show your answer to 4 decimal places.)
  3. The p-value is ? > ≤  αα
  4. Based on this, we should Select an answer reject fail to reject accept  the null hypothesis.
  5. Thus, the final conclusion is that ...
    • The data suggest the populaton proportion is significantly smaller than 14% at αα = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 14%
    • The data suggest the population proportion is not significantly smaller than 14% at αα = 0.05, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 14%.
    • The data suggest the population proportion is not significantly smaller than 14% at αα = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 14%.
  6. Interpret the p-value in the context of the study.
    • If the sample proportion of inner city residents who have sleep apnea is 12% and if another 359 inner city residents are surveyed then there would be a 13.47% chance of concluding that fewer than 14% of inner city residents have sleep apnea.
    •  There is a 14% chance of a Type I error
    • If the population proportion of inner city residents who have sleep apnea is 14% and if another 359 inner city residents are surveyed then there would be a 13.47% chance fewer than 12% of the 359 residents surveyed have sleep apnea.
    • There is a 13.47% chance that fewer than 14% of all inner city residents have sleep apnea.
  7. Interpret the level of significance in the context of the study.
    • If the population proportion of inner city residents who have sleep apnea is smaller than 14% and if another 359 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 14%.
    • There is a 5% chance that the proportion of all inner city residents who have sleep apnea is smaller than 14%.
    • 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 14% and if another 359 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 smaller than 14%.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman