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 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. B) 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 C) There is a 99% chance that the true value of p lies between 0.113 and 0.171. D) 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.

Answer 1

The correct answer is: A. 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.

Explanation:

A confidence interval is a range of values that is likely to contain the true value of a population parameter. In this case, the population parameter is the proportion of voters who favor a tax on e-commerce. The confidence interval is constructed from a sample of voters, and it is based on the assumption that the sample is representative of the population.

The 99% confidence interval means that if we were to take many different samples of size 250 and construct a confidence interval for each sample, 99% of the confidence intervals would contain the true value of the population proportion. This does not mean that there is a 99% chance that the true value of the population proportion lies between 0.113 and 0.171. It means that if we were to take many different samples of size 250 and construct a confidence interval for each sample, 99% of the confidence intervals would contain the true value of the population proportion.

The other answer choices are incorrect because they do not correctly interpret the meaning of a confidence interval.

Answer 2

The correct interpretation of the confidence interval is A) 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. This interpretation is in line with the frequentist approach to statistics, which states that the true value of the population parameter is fixed and unknown, and that a confidence interval provides a range of plausible values for this parameter based on the observed data. It is important to note that a confidence interval does not provide a probability that the true value of the parameter lies within the interval, but rather a measure of the precision of the estimate based on the sample data.