Complete Question
The complete question is shown on the first uploaded image
Answer:
a
The sample size is [tex]n =944[/tex]
b
The sample size is [tex]n_b = 1068[/tex]
Step-by-step explanation:
From the question we are told that
The proportion is mathematically represented as [tex]\r p = 0.33[/tex]
The marginal error is [tex]e = 0.03[/tex]
The confidence level is 95 % = 0.95
The z-value of the confidence level is
[tex]z_c = 1.96[/tex]
This value is obtained from the z table
The sample size is mathematically evaluated as
[tex]n = [\frac{z_c}{e} ]^2 * \r p(1- \r p)[/tex]
substituting values
[tex]n = [\frac{1.96}{0.03} ]^2 * 0.33 (1- 0.33)[/tex]
[tex]n =944[/tex]
If no estimate is available the let assume [tex]\r p = 0.50[/tex]
So
[tex]n_b = [\frac{z_c}{e} ]^2 * \r p(1- \r p)[/tex]
substituting values
[tex]n_b = [\frac{1.96}{0.03} ]^2 * 0.50 (1- 0.50)[/tex]
[tex]n_b = 1068[/tex]
