Answer:
The sample size is [tex]n = 2401[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E= 2\% = 0.02[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 5\% = 0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Let assume that the sample proportion is [tex]\r p = 0.5[/tex]
Generally the sample size is evaluated as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p ( 1- \r p )[/tex]
[tex]n = [\frac{1.96}{0.02} ]^2 * 0.5 ( 1- 0.5 )[/tex]
[tex]n = 2401[/tex]
