Solve the problem.
-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

Solve the problem.
-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

A confidence interval is not a statement about any one particular sample, but rather it is a statement about the procedure used to construct the interval. Statement B correctly interprets the meaning of the confidence interval as it is the only option that refers to the long run behavior of the confidence interval procedure. Option A is incorrect because it suggests that the procedure is exact and will produce identical confidence intervals exactly 99% of the time. Option C is incorrect because it suggests that the true value of p will necessarily lie in the interval between 0.113 and 0.171 for 99% of the samples, which is not true. Option D is incorrect because it incorrectly suggests that there is a probability associated with the true value of the parameter, p, which is not the case.

Solve the Problem. -A Researcher Is Interested in Estimating the Proportion of Voters