Asked by Sonia Nelson on Jun 27, 2024

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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.