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A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?

Respuesta :

Answer:1866

Step-by-step explanation:

Given

n=200

x=118

Population proportion P=[tex]\frac{118}{200}[/tex]=0.59

[tex]\alpha [/tex]=0.005

Realiability =99%

[tex]Z_{\frac{\alpha }{2}}=2.576[/tex]

Margin of erroe is given by [tex]\sqrt{\frac{p\left ( 1-p \right )}{N}}[/tex]

0.03= [tex]\sqrt{\frac{0.59\left ( 1-0.59 \right )}{N}}[/tex]

85.667=[tex]\sqrt{\frac{N}{0.6519}}[tex]

N=1865.88[tex]\approx 1866 Students[/tex]

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