Question

Washington (CNN) About three-quarters of Americans (77%) approve of President Donald Trump's decision to meet with North Korean leader Kim Jong Un, according to a new CNN pollconducted by SSRS. Trump's approval rating for handling the situation with North Korea has jumped 10 points since late March.

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The CNN Poll was conducted by SSRS May 2-5 among a random national sample of 1,015 adults reached on landlines or cellphones by a live interviewer. Results for the full sample have a margin of sampling error of plus or minus 3.6 percentage points; it is larger for subgroups.
Assuming that the level of confidence and the statistic remain the same what would happen to the Margin of Error if they had surveyed 2,030 adults instead of 1,015?
a. The margin of error would increase.
b. The margin of error would decrease.
c. The margin of error would stay the same.
d. It will depend on how the people in the sample respond.

Answer 1

b. The margin of error would decrease.

Explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval has the following format:

`M = z(\sigma)/(√(n))`

In which z is related to the confidence level,
`\sigma` is the standard deviation of the population and n is the size of the sample.

This means that the margin of error is inversely proportional to the size of the sample, which means that if the sample size increases, the margin of error decreases.

In this question, the sample size is increased, leading to a smaller margin of error. So the correct answer is given by option b.