51% of students entering four-year colleges receive a degreewithin six years. Is this percent smaller than for students whoplay intramural sports? 123 of the 292 students who playedintramural sports received a degree within six years. What can beconcluded at the level of significance of αα = 0.01?

1. For this study, we should use Select an answer t-test for apopulation mean z-test for a population proportion
2. The null and alternative hypotheses would be:
   Ho: ? p μ  Select an answer > < ≥ ≠ ≤=   (please enter a decimal)   
   H₁: ? p μ  Select an answer = ≥ > < ≠≤   (Please enter a decimal)

1. The test statistic ? z t  =  (please showyour answer to 3 decimal places.)
2. The p-value =  (Please show your answer to 4 decimalplaces.)
3. The p-value is ? ≤ >  αα
4. Based on this, we should Select an answer accept fail to rejectreject  the null hypothesis.
5. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantlysmaller than 51% at αα = 0.01, so there is sufficient evidence toconclude that the population proportion of students who playedintramural sports who received a degree within six years is equalto 51%.
   • The data suggest the populaton proportion is significantlysmaller than 51% at αα = 0.01, so there is sufficient evidence toconclude that the population proportion of students who playedintramural sports who received a degree within six years is smallerthan 51%
   • The data suggest the population proportion is not significantlysmaller than 51% at αα = 0.01, so there is not sufficient evidenceto conclude that the population proportion of students who playedintramural sports who received a degree within six years is smallerthan 51%.
6. Interpret the p-value in the context of the study.
   • There is a 51% chance of a Type I error.
   • There is a 0.12% chance that fewer than 51% of all students whoplayed intramural sports graduate within six years.
   • If the sample proportion of students who played intramuralsports who received a degree within six years is 42% and if another292 such students are surveyed then there would be a 0.12% chanceof concluding that fewer than 51% of all students who playedintramural sports received a degree within six years.
   • If the population proportion of students who played intramuralsports who received a degree within six years is 51% and if another292 students who played intramural sports are surveyed then therewould be a 0.12% chance fewer than 42% of the 292 students surveyedreceived a degree within six years.
7. Interpret the level of significance in the context of thestudy.
   • There is a 1% chance that the proportion of all students whoplayed intramural sports who received a degree within six years issmaller than 51%.
   • If the population proportion of students who played intramuralsports who received a degree within six years is 51% and if another292 students who played intramural sports are surveyed then therewould be a 1% chance that we would end up falsely concluding thatthe proportion of all students who played intramural sports whoreceived a degree within six years is smaller than 51%
   • There is a 1% chance that aliens have secretly taken over theearth and have cleverly disguised themselves as the presidents ofeach of the countries on earth.
   • If the population proportion of students who played intramuralsports who received a degree within six years is smaller than 51%and if another 292 students who played intramural sports aresurveyed then there would be a 1% chance that we would end upfalsely concluding that the proportion of all students who playedintramural sports who received a degree within six years is equalto 51%.