Question

A school administrator is interested in estimating the proportion of students in the district who participate in community service activities. From a random sample of 100 students in the district, the administrator will construct a 99 percent confidence interval for the proportion of all district students who participate in community service activities. Which of the following statements must be true?

A)The population proportion will be in the confidence interval.

b)The probability that the confidence interval will include the population proportion is 0.99.

c)The probability that the confidence interval will include the sample proportion is 0.99.

D)The population proportion and the sample proportion will be equal.

E)The probability that the population proportion and the sample proportion will be equal is 0.99.

Answer 1

The probability that the confidence interval will include the population proportion is 0.99.

Answer: Option B.

Step-by-step explanation:

In statistics, a confidence interval is a type of estimate computed from the statistics of the observed data. This proposes a range of plausible values for an unknown parameter. The interval has an associated confidence level that the true parameter is in the proposed range.

The purpose of taking a random sample from a lot or population and computing a statistic, such as the mean from the data, is to approximate the mean of the population. A confidence interval addresses this issue because it provides a range of values which is likely to contain the population parameter of interest.