Waulmodic 2 $$ C D=24= $$ The manager of a gym selected a sample of 139 members at random to estimate tre percentage of the grry members that would continue to pay for a membership if the price increased. From the surve, fte marager estimates tiat $$ 32 \% $$ of the gym's members would continue to pay for a membership if the price increased, with an awsciates margin of errof $$ 6.39 \% $$. If the survey is repeated with a random sample of 272 members and the resuits are calculated in the same way, which of the following will be the most likely effect of using the larger random sample comparsinter mater arder sample? A) The margin of error will be lower. B) The margin of error wit be higher C) The estimate of the percentage of the gym's members that would contrive topay for a mentessio fite pitas increased will be lower D) The estimate of the percentage of the gym's members that would cortinue to pay for a mententio fine pice: increased will be higher:

Question

UpStudy AI · Accepted Answer

The margin of error in a survey is influenced by the sample size. Specifically, for a proportion, the margin of error is calculated using the formula:

$$
\text{Margin of Error} = z \times \sqrt{\frac{p(1-p)}{n}}
$$

where:
- $$ z $$ is the z-score corresponding to the desired confidence level,
- $$ p $$ is the sample proportion,
- $$ n $$ is the sample size.

From the formula, it's clear that as the sample size $$ n $$ increases, the margin of error decreases because the standard error $$ \sqrt{\frac{p(1-p)}{n}} $$ becomes smaller.

In the given scenario:
- Original sample size ($$ n_1 $$) = 139, Margin of error = 6.39%
- New sample size ($$ n_2 $$) = 272

When the sample size increases from 139 to 272, the margin of error will decrease because the larger sample size provides a more precise estimate of the population proportion.

**Answer:**  
A) The margin of error will be lower.
Using a larger sample size will result in a lower margin of error.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Statistics Questions