Answer:
The sample size is [tex]n = 384 [/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.05[/tex]
Here we will assume that the sample proportion is [tex]\^ p = 0.5[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.96 }{0.05} ]^2 * 0.5 (1 - 0.5 ) [/tex]
=> [tex]n = 384 [/tex]
