A researcher is interested in estimating the proportion of voters who favor a tax on e-commerce. Based on a sample of 250 people, she obtains the following 99% confidence interval for the Population proportion p:
0.113

Question

A researcher is interested in estimating the proportion of voters who favor a tax on e-commerce. Based on a sample of 250 people, she obtains the following 99% confidence interval for the Population proportion p:
0.113 < p < 0.171 Which of the statements below is a valid interpretation of this confidence interval? 
A)If 100 different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, exactly 99 of these confidence intervals would contain the true
Value of p.
B)If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, in the long run 99% of the confidence intervals would contain the
True value of p.
C)If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, 99% of the time the true value of p would lie between 0.113 and
0.171
D)There is a 99% chance that the true value of p lies between 0.113 and 0.171

Quizplus · Accepted Answer

The correct interpretation of a confidence interval is that if many different samples were taken and a confidence interval calculated for each, a certain percentage (in this case, 99%) of those intervals would contain the true population parameter. This is a statement about the procedure of constructing confidence intervals, not about the probability of any one interval containing the parameter.

A Researcher Is Interested in Estimating the Proportion of Voters