According to a 2018 poll, 31% of adults from a certain region were very likely to watch some coverage of a certain sporting event on television. The survey polled 900 adults from the region and hi a margin of error of plus or minus 2 percentage points with a 99% level of confidence. Complete parts (a) through (c) below.
a. State the survey results in confidence interval form and interpret the interval.
The confidence interval of the survey results is (Round to two decimal places as needed.)
Interpret the interval. Choose the correct answer below.
• A. We are 99% confident that the percentage of adults in the region who were very likely to watch some of this sporting event on television is within the confidence interval.
• B. There is a 99% chance that the percentage of adults in the region who were very likely to watch some of this sporting event on television is within the confidence interval.
• c. The confidence interval will contain the percentage of adults in the region who were very likely to watch some of this sporting event on television 99% of the time.
O D. 99% of the 900 adults from the region that were polled fell within the confidence interval.
b. If the polling company was to conduct 200 such surveys of 900 adults from the region, how many of them would result in confidence intervals that included the true population proportion?
We would expect at least
of them to include the true population proportion.
c. Suppose a student wrote this interpretation of the confidence interval: "We are 99% confident that the sample proportion is within the confidence interval.* What, if anything, is incorrect in this interpretation?
• A. This interpretation is incorrect because the confidence level states the probability that the sample proportion is within the confidence interval.
• B. This interpretation is incorrect because a confidence interval is about a population not a sample.
• C. The interpretation is incorrect because the confidence level represents how often the confidence interval will not contain the correct population proportion.
• D. There is nothing wrong with this interpretation.