Answer:
The sample size is [tex]n =419[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.45[/tex]
The margin of error is [tex]E = 0.04[/tex]
Given that the confidence level is 90%
Then the level of significance can be mathematically represented as
[tex]\alpha = 100 -90[/tex]
[tex]\alpha = 10\%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the level of significance from the normal distribution table the value is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the sample size is mathematically represented as
[tex]n = [ \frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * p(1- p )[/tex]
substituting values
[tex]n = [ \frac{1.645 }{0.04} ]^2 * 0.45(1- 0.45 )[/tex]
[tex]n =419[/tex]
