48,747 views
12 votes
12 votes
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 ±​3%." The margin of error was based on a​ 95% confidence level. Fill in the blanks to obtain a correct interpretation of this confidence interval. We are​ ___________ confident that the​ ___________ of registered voters​ ___________ planning on voting for Robert Smith is between​ ___________ and​ ___________.

User Hakan SONMEZ
by
2.9k points

2 Answers

12 votes
12 votes

Final answer:

The confidence interval means we are 95% certain that the true proportion of voters for Robert Smith lies between 49% and 55%, adjusting for the margin of error of ±3%.

Step-by-step explanation:

We are 95% confident that the proportion of registered voters planning on voting for Robert Smith is between 49% and 55%.

This interpretation means that if we were to take many samples and construct a 95% confidence interval from each sample, we would expect 95% of those intervals to contain the true proportion of voters who favor Robert Smith. The reported margin of error of ±3% gives us the lower and upper bounds of this interval, which we obtain by subtracting and adding the margin of error from the sample proportion, respectively.

User Marc Alff
by
2.7k points
16 votes
16 votes

Answer:

We are 95% confident that the percentage of registered voters in the nation planning on voting for Robert Smith is between 49% and 55%.

Step-by-step explanation:

Given that :

Margin of Error = ±3%

Sample Proportion = 52%

Confidence level = 95%

The 95% confidence interval is :

Sample proportion ± margin of error

52% ± 3%

Lower boundary = 52% - 3% = 49%

Upper boundary = 52% + 3% = 55%

The interpretation is that at a given confidence level ; the popukation proportion based on the sample proportion and margin of error is in the confidence interval.

User Ackelry Xu
by
3.0k points