Answer:
The sample size is [tex]n =6697[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is p = 0.55
The margin of error is E = 0.01
Given that the confidence level is then the level of significance is mathematically represented as
[tex]\alpha = (100 -90)\%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645 [/tex]
Gnerally the sample size is mathematically represented as
[tex]n = \frac{[Z_{\frac{\alpha }{2} }]^2 * p(1-p)}{E^2}[/tex]
=> [tex]n = \frac{1.645^2 * 0.55(1-0.55)}{0.01^2}[/tex]
=> [tex]n = \frac{1.645^2 * 0.55(1-0.55)}{0.01^2}[/tex]
=> [tex]n =6697[/tex]
