15% 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 322 people from the inner city surveyed, 42 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 Select an answer z-test for a population proportion t-test for a population mean

The null and alternative hypotheses would be:
Ho: ? p μ  Select an answer > < = ≠   (please enter a decimal)
H₁: ? μ p  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 accept fail to reject  the null hypothesis.

Thus, the final conclusion is that ...

The data suggest the population proportion is not significantly smaller than 15% 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 15%.

The data suggest the population proportion is not significantly smaller than 15% 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 15%.

The data suggest the populaton proportion is significantly smaller than 15% 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 15%

Interpret the p-value in the context of the study.

If the sample proportion of inner city residents who have sleep apnea is 13% and if another 322 inner city residents are surveyed then there would be a 16.27% chance of concluding that fewer than 15% of inner city residents have sleep apnea.

There is a 15% chance of a Type I error

If the population proportion of inner city residents who have sleep apnea is 15% and if another 322 inner city residents are surveyed then there would be a 16.27% chance fewer than 13% of the 322 residents surveyed have sleep apnea.

There is a 16.27% chance that fewer than 15% of all inner city residents have sleep apnea.

Interpret the level of significance in the context of the study.

There is a 1% chance that the proportion of all inner city residents who have sleep apnea is smaller than 15%.

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.

If the population proportion of inner city residents who have sleep apnea is smaller than 15% and if another 322 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 15%.

If the population proportion of inner city residents who have sleep apnea is 15% and if another 322 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 15%.

Name: 15% of all Americans suffer from sleep apnea. A researcher suspects th
Uploaded: 2024-03-20T07:07:00.000Z
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Description: 15% 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 322 people from the inner city surveyed, 42 of them suffered from sleep apnea. What can be conclu

Question

15% 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 322 people from the inner city surveyed, 42 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 Select an answer z-test for a population proportion t-test for a population mean
The null and alternative hypotheses would be:
Ho: ? p μ Select an answer > < = ≠ (please enter a decimal)
H₁: ? μ p 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 accept fail to reject the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the population proportion is not significantly smaller than 15% 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 15%.
- The data suggest the population proportion is not significantly smaller than 15% 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 15%.
- The data suggest the populaton proportion is significantly smaller than 15% 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 15%
Interpret the p-value in the context of the study.
- If the sample proportion of inner city residents who have sleep apnea is 13% and if another 322 inner city residents are surveyed then there would be a 16.27% chance of concluding that fewer than 15% of inner city residents have sleep apnea.
1. - There is a 15% chance of a Type I error
  - If the population proportion of inner city residents who have sleep apnea is 15% and if another 322 inner city residents are surveyed then there would be a 16.27% chance fewer than 13% of the 322 residents surveyed have sleep apnea.
  - There is a 16.27% chance that fewer than 15% of all inner city residents have sleep apnea.
2. Interpret the level of significance in the context of the study.
  - There is a 1% chance that the proportion of all inner city residents who have sleep apnea is smaller than 15%.
  - 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.
  - If the population proportion of inner city residents who have sleep apnea is smaller than 15% and if another 322 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 15%.
  - If the population proportion of inner city residents who have sleep apnea is 15% and if another 322 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 15%.

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