Question

13

50% of students entering four-year colleges receive a degree within six years. Is this percent different from for students who play intramural sports? 146 of the 256 students who played intramural sports received a degree within six years. 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)

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer accept reject fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly different from 50% at αα = 0.05, so there is sufficient evidence to conclude that the population proportion of students who played intramural sports who received a degree within six years is equal to 50%.
   • The data suggest the populaton proportion is significantly different from 50% at αα = 0.05, so there is sufficient evidence to conclude that the population proportion of students who played intramural sports who received a degree within six years is different from 50%
   • The data suggest the population proportion is not significantly different from 50% at αα = 0.05, so there is not sufficient evidence to conclude that the population proportion of students who played intramural sports who received a degree within six years is different from 50%.
8. Interpret the p-value in the context of the study.
   • There is a 2.44% chance that the percent of all students who played intramural sports who received a degree within six years differs from 50%.
   • If the population proportion of students who played intramural sports who received a degree within six years is 50% and if another 256 students who played intramural sports are surveyed then there would be a 2.44% chance that either more than 57% of the 256 studetns surveyed received a degree within six years or fewer than 43% of the 256 students surveyed received a degree within six years.
   • There is a 2.44% chance of a Type I error.
   • If the sample proportion of students who played intramural sports who received a degree within six years is 57% and if another 256 voters are surveyed then there would be a 2.44% chance that we would conclude either fewer than 50% of all students who played intramural sports received a degree within six years or more than 50% of all students who played intramural sports received a degree within six years.
9. Interpret the level of significance in the context of the study.
   • If the population proportion of students who played intramural sports who received a degree within six years is 50% and if another 256 students who played intramural sports are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all students who played intramural sports who received a degree within six years is different from 50%
   • 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.
   • There is a 5% chance that the proportion of all students who played intramural sports who received a degree within six years is different from 50%.
   • If the population proportion of students who played intramural sports who received a degree within six years is different from 50% and if another 256 students who played intramural sports are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all students who played intramural sports who received a degree within six years is equal to 50%.

14

10% 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 352 people from the inner city surveyed, 21 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 t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:
   Ho: ? μ p  Select an answer < ≠ = >   (please enter a decimal)   
   H₁: ? μ p  Select an answer ≠ > = <   (Please enter a decimal)

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? > ≤  αα
6. Based on this, we should Select an answer reject accept fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the populaton proportion is significantly smaller than 10% 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 10%
   • The data suggest the population proportion is not significantly smaller than 10% 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 10%.
   • The data suggest the population proportion is not significantly smaller than 10% 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 10%.
8. Interpret the p-value in the context of the study.
   • If the sample proportion of inner city residents who have sleep apnea is 6% and if another 352 inner city residents are surveyed then there would be a 0.58% chance of concluding that fewer than 10% of inner city residents have sleep apnea.
   • If the population proportion of inner city residents who have sleep apnea is 10% and if another 352 inner city residents are surveyed then there would be a 0.58% chance fewer than 6% of the 352 residents surveyed have sleep apnea.
   • There is a 10% chance of a Type I error
   • There is a 0.58% chance that fewer than 10% of all inner city residents have sleep apnea.
9. Interpret the level of significance in the context of the study.
   • 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 10% and if another 352 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 10%.
   • If the population proportion of inner city residents who have sleep apnea is smaller than 10% and if another 352 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 10%.
   • There is a 5% chance that the proportion of all inner city residents who have sleep apnea is smaller than 10%.

Answer 1

Solution:-) The condition for the proportion of z test are satisfied. Let p be the proportion of students who played intramural sports received a degree within six years.

n = 259 and p = 0.5703

Hence the condition are satisfied for proportion z test

e) The data suggest the populaton proportion is significantly different from 50% at α = 0.05, so there is sufficient evidence to conclude that the population proportion of students who played intramural sports who received a degree within six years is different from 50%

f) The p-value interprets that there is a 2.44% chance that the percent of all students who played intramural sports who received a degree within six years differs from 50%.

g) Level of significance indicates the probability of rejecting null hypothesis given that null hypothesis is true.

If the population proportion of students who played intramural sports who received a degree within six years is different from 50% and if another 256 students who played intramural sports are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all students who played intramural sports who received a degree within six years is equal to 50%.

2)Let p be the proportion of Americans suffer from sleep apnea

n = 352 and p = 0.5703

We can use the z proportion test