(Solved): q6  5\% of students entering four-year colleges receive a degree within six years. Is this perc ...

5\% of students entering four-year colleges receive a degree within six years. Is this percent smaller than or students who play intramural sports? 125 of the 236 students who played intramural sports received a legree within six years. What can be concluded at the level of significance of \( \alpha=0.05 \) ? a. For this study, we should use b. The null and alternative hypotheses would be: \begin{tabular}{l|l|l} Ho: & (please enter a decimal) \\ \( \mathrm{H}_{1}: \) & (Please enter a decimal) \end{tabular} c. The test statistic = \( \quad \) (please show your answer to 3 decimal places.) d. The \( p \)-value \( =\quad \) (Please show your answer to 4 decimal places.) e. The p-value is \( \alpha \) f. Based on this, we should g. Thus, the final conclusion is that ... The data suggest the populaton proportion is significantly smaller than \( 55 \% \) at \( \alpha=0.05 \), 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 smaller than \( 55 \% \) The data suggest the population proportion is not significantly smaller than \( 55 \% \) at \( \alpha=0.05 \), 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 smaller than \( 55 \% \). The data suggest the population proportion is not significantly smaller than \( 55 \% \) at \( \alpha=0.05 \), 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 \( \mathrm{p} \)-value in the context of the study. There is a \( 26.5 \% \) chance that fewer than \( 55 \% \) of all students who played intramural sports graduate within six years. If the sample proportion of students who played intramural sports who received a degree within six years is \( 53 \% \) and if another 236 such students are surveyed then there would be a \( 26.5 \% \) chance of concluding that fewer than \( 55 \% \) of all students who played intramural sports received a degree within six years. There is a 55\% 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 236 students who played intramural sports are surveyed then there would be a \( 26.5 \% \) chance fewer than \( 53 \% \) of the 236 students surveyed received a dearee within six vears. If the population proportion of students who played intramural sports who received a degree within six years is \( 55 \% \) and if another 236 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 smaller than \( 55 \% \) There is a \( 5 \% \) chance that the proportion of all students who played intramural sports who received a degree within six years is smaller than \( 55 \% \). If the population proportion of students who played intramural sports who received a degree within six years is smaller than \( 55 \% \) and if another 236 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 aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth.