A University Wants to Increase Its Retention Rate of 4 $\mathrm { H } _ { 0 }$

A university wants to increase its retention rate of 4% for graduating students from the previous year.After implementing several new programs during the last two years,the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%.Test an appropriate hypothesis and state your conclusion.Be sure the appropriate assumptions and conditions are satisfied before you proceed.

A) $\mathrm { H } _ { 0 }$ : p = 0.04; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.04; z = 0.96; P-value = 0.1685.This data shows virtually no evidence that more than 4% of students are retained; the university should not continue with the new programs.
B) $\mathrm { H } _ { 0 }$ : p = 0.04; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.04; z = 1.07; P-value = 0.8577.This data shows conclusive evidence that more than 4% of students are retained; therefore,the university should continue with the new programs.
C) $\mathrm { H } _ { 0 }$ : p = 0.04; $\mathrm { H } _ { \mathrm { A } }$ : p < 0.04; z = -1.07; P-value = 0.8577.This data shows conclusive evidence that more than 4% of students are retained; the university should continue with the new programs.
D) $\mathrm { H } _ { 0 }$ : p = 0.04; $\mathrm { H } _ { \mathrm { A } }$ : p > 0.04; z = -1.07; P-value = 0.1423.This data does not show that more than 4% of students are retained; the university should not continue with the new programs.
E) $\mathrm { H } _ { 0 }$ : p = 0.04; $\mathrm { H } _ { \mathrm { A } }$ : p ? 0.04; z = 1.07; P-value = 0.2846.This data shows virtually no evidence that more than 4% of students are retained; the university should not continue with the new programs.