Days before a presidential election, a nationwide random sample of registered voters was taken. Based on this random sample, it was reported that "52% of registered voters plan on voting for Robert Smith with a margin of error of plus or minus± 3%." The margin of error was based on a 95% confidence level. Can we say with 95% confidence that Robert Smith will win the election if he needs a simple majority of votes to win? Choose the correct answer below.

A. No, because the margin of error can never be more than 1%.

B. Yes, because 50% is within the bounds of the confidence interval.

C. Yes, since over 50% of the voters in the sample say they will vote for Robert Smith.

D. No, because 50% is within the bounds of the confidence interval.

Question

Mathematics

Lynn

3 March, 17:45

Days before a presidential election, a nationwide random sample of registered voters was taken. Based on this random sample, it was reported that "52% of registered voters plan on voting for Robert Smith with a margin of error of plus or minus± 3%." The margin of error was based on a 95% confidence level. Can we say with 95% confidence that Robert Smith will win the election if he needs a simple majority of votes to win? Choose the correct answer below.

A. No, because the margin of error can never be more than 1%.

B. Yes, because 50% is within the bounds of the confidence interval.

C. Yes, since over 50% of the voters in the sample say they will vote for Robert Smith.

D. No, because 50% is within the bounds of the confidence interval.

+1

Answers (2)

Know the Answer?

Ariel West · Answer 1

D. No, because 50% is within the bounds of the confidence interval.

Step-by-step explanation:

"52% of registered voters plan on voting for Robert Smith with a margin of error of plus or minus± 3%"

This means that the 95% confidence interval for the percentage of people that plan on voting for Robert Smith is

(52-3 = 49%, 52+3 = 55%).

We can't say that he will win the election, because at the 95% confidence level, the proportion is not guaranteed to be above 50%.

So the correct answer is:

D. No, because 50% is within the bounds of the confidence interval.

Aryanna Holden · Answer 2

D. No, because 50% is within the bounds of the confidence interval.

Step-by-step explanation:

"52% of registered voters plan on voting for Robert Smith with a margin of error of plus or minus± 3%." means that

There is 95% probability that Robert Smith is voted between 49% and 55%. Majority of votes is needed to win the election, but this confidence interval doesn't guarantee 50+% vote.

Therefore we cannot say Robert Smith will win the election with this 95% confidence interval.