Question

A state 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%. Find the minimum sample size such that the desired type one error is 0.01 and type two error is 0.01 when the true retention rate is 4.5%.

Answer 1

Hypothesized proportion      =p o					=	0.04
true proportion                          =pa					=	0.04
for 0.01 level and left tailed test critival value Zα					=	2.33
for 0.01 level of type II error critival value Zβ					=	2.33
required sample size             =n=				((zα(√po(1-po)+zβ(√pa(1-pa))/(p-po))2
					=	35204.00