A political candidate has asked you to conduct a poll to determine what percentage of people support her.
If the candidate only wants a margin of error at a confidence level, what is the minimum sample
size needed?
Give your answer in whole people.

Ask by Mann Riley. in the United States

Mar 24,2025

Question

A political candidate has asked you to conduct a poll to determine what percentage of people support her.
If the candidate only wants a margin of error at a confidence level, what is the minimum sample
size needed?
Give your answer in whole people.

Ask by Mann Riley. in the United States

Mar 24,2025

UpStudy AI · Accepted Answer

We start with the margin of error formula for a proportion:

$$
ME = z \cdot \sqrt{\frac{p(1-p)}{n}}
$$

Since the candidate wants the most conservative (largest) sample size, we use $$ p = 0.5 $$ (which maximizes $$ p(1-p) $$) and a $$ 95\% $$ confidence level gives $$ z = 1.96 $$. The margin of error is given as $$ ME = 0.01 $$.

Substitute these values into the formula and solve for $$ n $$:

$$
0.01 = 1.96 \cdot \sqrt{\frac{0.5 \times 0.5}{n}} \quad \Rightarrow \quad 0.01 = 1.96 \cdot \sqrt{\frac{0.25}{n}}
$$

Square both sides to eliminate the square root:

$$
(0.01)^2 = (1.96)^2 \cdot \frac{0.25}{n}
$$

$$
0.0001 = 3.8416 \cdot \frac{0.25}{n}
$$

Multiply $$ 3.8416 $$ and $$ 0.25 $$:

$$
0.0001 = \frac{0.9604}{n}
$$

Now, solve for $$ n $$ by multiplying both sides by $$ n $$ and dividing by $$ 0.0001 $$:

$$
n = \frac{0.9604}{0.0001} = 9604
$$

Thus, the minimum sample size needed is:

$$
\mathrm{n} = 9604
$$
The minimum sample size needed is 9604 people.

A political candidate has asked you to conduct a poll to determine what percentage of people support her.
If the candidate only wants a margin of error at a confidence level, what is the minimum sample
size needed?
Give your answer in whole people.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Statistics Questions

A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a margin of error at a confidence level, what is the minimum sample size needed? Give your answer in whole people.

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Statistics Questions

A political candidate has asked you to conduct a poll to determine what percentage of people support her.
If the candidate only wants a margin of error at a confidence level, what is the minimum sample
size needed?
Give your answer in whole people.