Question

50% of students entering four-year colleges receive a degree within six years. Is this percent larger than for students who play intramural sports? 118 of the 218 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: ? p μ  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 reject fail to reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the populaton proportion is significantly larger than 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 larger than 50%
   • The data suggest the population proportion is not significantly larger than 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 larger than 50%.
   • The data suggest the population proportion is not significantly larger than 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%.
8. Interpret the p-value in the context of the study.
   • There is a 11.14% chance that more than 50% of all students who played intramural sports received a degree within six years.
   • If the sample proportion of students who played intramural sports who received a degree within six years is 54% and if another 218 students who played intramural sports are surveyed then there would be a 11.14% chance of concluding that more than 50% of all students who played intramural sports received a degree within six years.
   • If the population proportion of students who played intramural sports who received a degree within six years is 50% and if another 218 students who played intramural sports are surveyed then there would be a 11.14% chance that more than 54% of the 218 students surveyed received a degree within six years
   • There is a 11.14% 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 50% and if another 218 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 larger than 50%
   • There is a 5% chance that the proportion of all students who played intramural sports who received a degree within six years is larger than 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.
   • If the population proportion of students who played intramural sports who received a degree within six years is larger than 50% and if another 218 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%.

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