Question

a student was asked to find a 98% confidence interval for the proportion of students who take notes using data from a random sample of size ( n = 79 ). which of the following is a correct interpretation of the interval ( 0.13 < p < 0.24 )?
there is a 98% chance that the proportion of the sample is between 0.13 and 0.24.
the proportion of all students who take notes is between 0.13 and 0.24, 98% of the time.
there is a 98% chance that the proportion of notetakers in a sample of 79 students will be between 0.13 and 0.24.
with 98% confidence, a randomly selected student takes notes in their classes with a proportion between 0.13 and 0.24.
with 98% confidence, the proportion of all students who take notes is between 0.13 and 0.24.
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Explanation:

A confidence interval gives an estimate of where the population parameter (in this case, the proportion of all students who take notes, denoted as \(p\)) lies. A 98% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, about 98% of those intervals would contain the true population parameter.

• The first option is incorrect because the confidence interval is about the population proportion, not the sample proportion. The sample proportion is a single - value (a point estimate) used to calculate the interval.
• The second option is incorrect. The proportion of all students who take notes is a fixed value (either it is within the interval or not). It does not change over time.
• The third option is incorrect. Similar to the first option, it is about the population proportion, not the proportion in a single sample.
• The fourth option is incorrect. A confidence interval is about a proportion of a population, not about a single - selected student.
• The fifth option is correct. A 98% confidence interval \(0.13 < p<0.24\) means that with 98% confidence, the proportion of all students who take notes (\(p\)) is between 0.13 and 0.24.

Answer:

With 98% confidence, the proportion of all students who take notes is between 0.13 and 0.24.