Respuesta :
Answer:
[tex]$ SE = 1.96\cdot \sqrt{\frac{0.50(1-0.50)}{2222} } $[/tex]
[tex]SE = 1.96\cdot 0.0106 \\\\SE = 0.021\\\\SE = 2.1 \: \%[/tex]
The correct option is
(c) 2.1%
Therefore, with a sample size of 2,222, the researcher can be 95% confident that the obtained sample proportion will differ from the true proportion (p) by no more than 2.1%
Step-by-step explanation:
The obtained sample proportion will differ from the true proportion (p) by
[tex]$ SE = z\cdot \sqrt{\frac{p(1-p)}{n} } $[/tex]
It is known as standard error or margin of error.
Where p is the sample proportion and n is the sample size.
Since we are not given p then we would assume
p = 0.50
That would maximize the error just to be on the safe side.
The z-score corresponding to 95% confidence level is given by
Level of significance = 1 - 0.95 = 0.05/2 = 0.025
From the z-table, the z-score corresponding to probability of 0.025 is
z-score = 1.96
So the error is
[tex]$ SE = 1.96\cdot \sqrt{\frac{0.50(1-0.50)}{2222} } $[/tex]
[tex]SE = 1.96\cdot 0.0106 \\\\SE = 0.021\\\\SE = 2.1 \: \%[/tex]
So the correct option is
(c) 2.1%
Therefore, with a sample size of 2,222, the researcher can be 95% confident that the obtained sample proportion will differ from the true proportion (p) by no more than 2.1%
