The manager of a gym selected a sample of $130$ members at random to …

Question

Prompt

The manager of a gym selected a sample of

130

members at random to estimate the percentage of the gym's members that would continue to pay for a membership if the price increased. From the survey, the manager estimates that

82%

of the gym's members would continue to pay for a membership if the price increased, with an associated margin of error of

6.39%

. If the survey is repeated with a random sample of

278

members and the results are calculated in the same way, which of the following will be the most likely effect of using the larger random sample compared to the smaller random sample?

The margin of error will be lower.

The margin of error will be higher.

The estimate of the percentage of the gym's members that would continue to pay for a membership if the price increased will be lower.

The estimate of the percentage of the gym's members that would continue to pay for a membership if the price increased will be higher.