Answer:
Check Explanation
Step-by-step explanation:
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
The population proportion can take on any value within the confidence interval obtained.
So, for each candidate, we can calculate the confidence interval for the population proportion of popular votes they would each receive.
For candidate A,
Sample Proportion = 47%
Margin of Error = 2%
Confidence Interval = (47%) ± (2%)
Confidence interval = (45%, 49%)
For candidate B,
Sample Proportion = 46%
Margin of Error = 2%
Confidence Interval = (46%) ± (2%)
Confidence interval = (44%, 48%)
The true proportion of popular votes for the two candidates will lie between
Confidence Interval for candidate A
(45%, 49%)
Confidence Interval for candidate B
(44%, 48%)
So, the true proportion of popular votes for candidate A can take on any value from 45% to 49%, and that for candidate B can take on values from 44% to 48%.
Because, A could have 45% and B have 48% or A could have 47% and B too have 47%.
The clear winner cannot be determined from this confidence interval obtained from the survey, it really is too close to call!
Hope this Helps!!!
