Question

We would like to estimate the proportion of UF students who owns a scooter to within 1% of the truth, with 95% confidence. We don't really have any idea what proportion does. How many students should be sampled? O 9604 O 19208 O 2401 O 384

Answer 1

Answer:

Option A) 9604

Step-by-step explanation:

We are given the following in the question:

Confidence level = 95%

Standard error = 1%

$p = q = 0.5$

Formula for sample size:

$n = (z_{stat}\times \dfrac{p(1-p)}{\text{Standard error}})^2$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get,

$n = (1.96\times \dfrac{0.5(1-0.5)}{0.01})^2 = 9604$

Thus, the sample size must be

Option A) 9604

Answer 2

The required sample size of the student is 9604

The formula needed to get the number of students sampled is expressed as:

$n=(z \times \frac{p(1-p)}{e} )^2$

p is the probability value = 0.5

e is the standard error = 1% = 0.01

z is the z-score at 95% interval = 1.96

Substitute the given parameters into the formula to have:

$n=(1.96 \times \frac{0.5(1-0.5)}{0.01} )^2\\n=(1.96\times \frac{0.475}{0.01})^2\\n=(1.96 \times 47.5)^2\\n= 93.1^2\\n=9604$

Hence the required sample size of the student is 9604

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