Question

a polistar wishes to estimate the number of left - handed scientists. what size sample should be obtained in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 3%? a previous study indicates that the proportion of left - handed scientists is 11%. round up to the nearest whole number.

oa. 418
ob. 589
oc. 662
od. 14

Explanation:

Step1: Find the critical value \(z_{\alpha/2}\)

For a \(98\%\) confidence level, \(\alpha = 1 - 0.98=0.02\), and \(\alpha/2 = 0.01\).
Using the standard normal distribution table or a calculator, \(z_{\alpha/2}=z_{0.01}\approx 2.33\)

Step2: Identify the values of \(p\) and \(E\)

Given \(p = 0.11\) (from the previous study indicating \(11\%\) left - handed scientists) and \(E=0.03\) (the margin of error \(3\%\))

Step3: Use the formula for sample size \(n\)

The formula for sample size when estimating a proportion is \(n=\frac{z_{\alpha/2}^{2}\times p\times(1 - p)}{E^{2}}\)
Substitute the values:

$$
LATEXBLOCK0
$$

Since we round up to the nearest whole number.

Answer:

B. 589