Question

Hugo polled 100 randomly selected people to see if they had exercised that week and found that 85% said they had. Lily asked 400 randomly selected people the same question and found that 85% of them also responded that they had exercised that week. If Hugo and Lily use a 99% confidence level (z*score of 2.58), which statement is true? E = z*
- Hugo’s margin of error will be exactly 2 times as large as Lily’s margin of error.
- Lily’s margin of error will be exactly 2 times as large as Hugo’s margin of error.
- Hugo’s margin of error will be exactly 4 times as large as Lily’s margin of error. - Lily’s margin of error will be exactly 4 times as large as Hugo’s margin of error.

Answer 1

Hugo polled 100 randomly selected people to see if they had exercised that week and found that 85% said they had. Lily asked 400 randomly selected people the same question and found that 85% of them also responded that they had exercised that week. If Hugo and Lily use a 99% confidence level, then the true statement will be

Hugo's margin of error will be exactly 2 times as large as Lily's margin of error.

Answer 2

Answer:

The true statement is : Hugo’s margin of error will be exactly 2 times as large as Lily’s margin of error.

Step-by-step explanation:

$\text{Margin of error : }\frac{\sigma \cdot z^*}{\sqrt n}.........,z^*=2.58\text{ for 99 percent level of confidence}$

And value of sigma is same as the response in both the cases is 85%

Hugo's margin of error : n = 100

$\text{Margin of error of Hugo : }\frac{\sigma \cdot z^*}{\sqrt {100}}\\\\=0.258\times \sigma$

Lilly's margin of error : n = 400

$\text{Margin of error of Lily : }\frac{\sigma \cdot z^*}{\sqrt {400}}\\\\=0.129\times \sigma\\\\=\frac{1}{2}\times 0.258\times \sigma\\\\=\frac{1}{2}\times\text{ Hugo's margin of error}$

Hence, the correct statement is : Hugo’s margin of error will be exactly 2 times as large as Lily’s margin of error.