Question

From a random sample of potential voters in an upcoming election, 47% indicated they intended to vote for Candidate R. A 95 percent confidence interval was constructed from the sample and the margin of error for the estimate of 5%. Which of the following is the best interpretation of the interval?

A) We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%

B) We are 95% confident that the proportion who intend to vote for Candidate R from the population is between 42% and 52%

C) We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is 47%

D) We are 95% confident that the proportion who intend to vote for Candidate R from the population is 47%

E)We are confident that 95% of the population intended to vote for Candidate R

Answer 1

Solution:

Given: From a random sample of potential voters in an upcoming election, 47% indicated they intended to vote for Candidate R.

Thus sample proportion =

c = confidence level = 95%

E = Margin of Error = 5%

Thus 95% confidence interval is:

Confidence interval is used to estimate population parameter like population mean , population variance , population proportion and it is expressed in interval form, from lower limit to upper limit with its confidence level.

Option A says about Sample proportion not the population proportion. Thus option A is incorrect.

Option B says about population proportion with given confidence level.

Thus correct answer is:

B) We are 95% confident that the proportion who intend to vote for Candidate R from the population is between 42% and 52%

Confidence interval is an interval from lower limit to upper limit, it is not about just point estimate and since option C and D are just about point estimate, both are incorrect.

Confidence level is the level at which we are confident about population parameter that will fall within the limits , it is not the part of proportion, thus option E is also incorrect.