Question

A margin of error is sometimes reported along with the results of a survey. An unbiased poll of 2000 cell phone users found that 78% favored the president. The margin of error was ±2%. If 35,000 cell phone users are surveyed, what is the maximum number of users who favored the president?

Answer 1

Using the upper limit of the initial survey's confidence interval (78% favor + 2% margin of error), the maximum number of users who favored the president out of 35,000, rounded to the next higher value, is 28,000.

Step-by-step explanation:

The question asks to calculate the maximum number of cell phone users who favored the president in a survey, given a certain percentage and a margin of error, when the sample size is increased. Given that the initial survey of 2000 users showed 78% in favor with a ±2% margin of error, and we want to find the maximum number for a larger survey of 35,000 users, we would use the upper limit of the confidence interval from the original survey.

First, to find the upper limit percentage, we add the margin of error to the observed percentage:

78% + 2% = 80%

Next, we apply this percentage to the new sample size:

35,000 users × 80% = 28,000 users

Therefore, the maximum number of cell phone users who favored the president, with rounding to the next higher value, is 28,000.

It is important to understand that an increased sample size does not change the original poll's reported margin of error directly. However, increasing the sample size can potentially decrease the margin of error for this new sample size if it were calculated. But since the new margin of error is not given, we use the margin of error from the original survey.