Question

51% of students entering four-year colleges receive a degree within six years. Is this percent different from for students who play intramural sports? 120 of the 230 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 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 accept reject fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the populaton proportion is significantly different from 51% 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 51%
   • The data suggest the population proportion is not significantly different from 51% 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 51%.
   • The data suggest the population proportion is not significantly different from 51% 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 51%.
8. Interpret the p-value in the context of the study.
   • If the population proportion of students who played intramural sports who received a degree within six years is 51% and if another 230 students who played intramural sports are surveyed then there would be a 72.18% chance that either more than 52% of the 230 studetns surveyed received a degree within six years or fewer than 50% of the 230 students surveyed received a degree within six years.
   • If the sample proportion of students who played intramural sports who received a degree within six years is 52% and if another 230 voters are surveyed then there would be a 72.18% chance that we would conclude either fewer than 51% of all students who played intramural sports received a degree within six years or more than 51% of all students who played intramural sports received a degree within six years.
   • There is a 72.18% chance that the percent of all students who played intramural sports who received a degree within six years differs from 51%.
   • There is a 72.18% chance of a Type I error.
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 51% and if another 230 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 51%
   • 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 51%.
   • If the population proportion of students who played intramural sports who received a degree within six years is different from 51% and if another 230 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 51%.
   • 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.

Answer 1

we are instructed to alnswer only first 4 sub part of the problem, In spite of it I did somewhat more.