When a website asks you to agree to a privacy policy, do you actually read the policy before agreeing?
Researchers asked people in a representative sample of 4,273 adults in the United States if they read
privacy policies and found that 920 said they always or often read them.
Use the five-step process for estimation problems (EMC ) to construct a 99% confidence interval for the
proportion of adults in the United States who always or often read privacy policies. (Enter your answer
using interval notation. Round your numerical values to three decimal places.)
Interpret the interval.
(a) There is a 99% chance that the true proportion of adults in the U.S. who always or often read
privacy policies falls within this interval.
(b) We are 99% confident that the true proportion of adults in the U.S. who always or often read
privacy policies falls directly in the middle of this interval.
(c) There is a 99% chance that the true proportion of adults in the U.S. who always or often read
privacy policies falls directly in the middle of this interval.
(d) We are 99% confident that the mean number of adults in the U.S. who always or often read
privacy policies falls within this interval.
(e) We are 99% confident that the true proportion of adults in the U.S. who always or often read
privacy policies falls within this interval.
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The correct interpretation is:
(e) We are 99% confident that the true proportion of adults in the U.S. who always or often read privacy policies falls within this interval.
Explanation:
A confidence interval is used to estimate an unknown population parameter (in this case, the proportion of adults in the U.S. who always or often read privacy policies) based on sample data. The interval provides a range within which the true population parameter is likely to fall with a certain level of confidence (in this case, 99%).
Since the interval is constructed using a sample survey, it provides an estimate of the true proportion. However, we cannot say with certainty that the true proportion falls within the interval, hence the use of the term "confident" rather than "certain".