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,  Which of the statements below is a valid interpretation of this confidence interval?

Group of answer choices

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, 99% of the time the true value of p would lie between 0.113 and 0.171.

C) 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.

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

Answer 1

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)

[ we can also say that,

if 100 samples of size 250 were selected and, based on each sample, a confidence interval were constructed, then 99 of the confidence interval are supposed to contain the true population proportion p ]

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