Question

55% of students entering four-year colleges receive a degree within six years. Is this percent larger than for students who play intramural sports? 170 of the 299 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of α = 0.05?

a. For this study, we should use (t-test for a population mean, z-test for population proportion)

b. The null and alternative hypotheses would be:

Ho: ( p, μ) ( ?,=, <, ≠, >) (please enter a decimal)   
H₁: ( μ, p) ( ?, <, =, >, ≠) (Please enter a decimal)

c. The test statistic ( t, z) = (please show your answer to 3 decimal places.)

d. The p-value = (Please show your answer to 4 decimal places.)

e. The p-value is ( ≤,>) α

f. Based on this, we should Select an answer (reject, fail to reject, accept the null hypothesis.

g. Thus, the final conclusion is that ...

• *The data suggest the populaton proportion is significantly larger than 55% 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 55%.
• *The data suggest the population proportion is not significantly larger than 55% 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 55%.
• *The data suggest the population proportion is not significantly larger than 55% 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 55%.

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

• * If the sample proportion of students who played intramural sports who received a degree within six years is 57% and if another 299 students who played intramural sports are surveyed then there would be a 25.94% chance of concluding that more than 55% of all students who played intramural sports received a degree within six years.
• *There is a 25.94% chance of a Type I error.
• *If the population proportion of students who played intramural sports who received a degree within six years is 55% and if another 299 students who played intramural sports are surveyed then there would be a 25.94% chance that more than 57% of the 299 students surveyed received a degree within six years.
• *There is a 25.94% chance that more than 55% of all students who played intramural sports received a degree within six years.

i.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 55% and if another 299 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 55%.
• *If the population proportion of students who played intramural sports who received a degree within six years is larger than 55% and if another 299 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 55%.
• *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 55%.
• *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

g)

The data suggest the population proportion is not significantly larger than 55% 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 55%.