Question

*50 pts!! WILL MARK BRAINLIEST*
Peter writes a blog covering news from his local area. He placed a survey on his blog asking whether users desired a change to his blog’s design. A total of 240 users took the survey on a day when the website had 2,975 visitors. Peter found that 55% of those surveyed were in favor of changing the design. Assuming a 90% confidence level, which of the following statements holds true?

A: As the sample size is appropriately large, the margin of error is ±0.053.
B:As the sample size is appropriately large, the margin of error is ±0.063.
C:As the sample size is too small, the margin of error cannot be trusted.
D:As the sample size is too small, the margin of error is ±0.053.

Answer 1

We don’t know the value for the population, so we must estimate the standard error using the data from the sample. Standard error = sqrt(p(1 - p)/n), where p is the proportion of yes and n is sample size. Margin of error = z* * standard error, z* = 1.64, so margin of error is 0.053. A sample size less than 10% of the population is needed to make an inference, thus, d is the correct answer. If this was confusing, please don’t hesitate to comment, hope this helps!

Answer 2

A: As the sample size is appropriately large, the margin of error is ±0.053.